audio audioduration (s) 0.83 21 | transcription stringlengths 3 127 | LaTeX stringlengths 7 142 | Source stringclasses 89
values |
|---|---|---|---|
y equals x squared | $\displaystyle y=x^{2}$ | https://www.youtube.com/watch?v=xrypSZU8cBE | |
dy equals 2x dx | $dy=2xdx$ | https://www.youtube.com/watch?v=xrypSZU8cBE | |
F dot t dS | $(F\cdot t dS)$ | https://www.youtube.com/watch?v=xrypSZU8cBE | |
x cubed plus y to the fifth | $x^{3}+y^{5}$ | https://www.youtube.com/watch?v=xrypSZU8cBE | |
xi plus yj | $x\mathbf{i}+y\mathbf{j}$ | https://www.youtube.com/watch?v=xrypSZU8cBE | |
integral of x dx plus y dy | $\int x\,dx+y\,dy$ | https://www.youtube.com/watch?v=xrypSZU8cBE | |
2pi a squared | $2\pi a^{2}$ | https://www.youtube.com/watch?v=xrypSZU8cBE | |
dx is negative a sine theta d theta | $dx=-a\sin\theta d\theta$ | https://www.youtube.com/watch?v=xrypSZU8cBE | |
integral from 0 to 2pi of a squared times sine squared theta plus cosine squared theta d theta | $\displaystyle \int_{0}^{2\pi}a^{2}(\sin^{2}\theta+\cos^{2}\theta)d\theta$ | https://www.youtube.com/watch?v=xrypSZU8cBE | |
one-half of sine two theta | $\frac{1}{2}(\sin2\theta)$ | https://www.youtube.com/watch?v=o7UCBjGsRTE | |
f sub x dx plus f sub y dy | $f_{x}dx+f_{y}dy$ | https://www.youtube.com/watch?v=o7UCBjGsRTE | |
dx becomes x prime of t dt | $\displaystyle d\mathbf{x}=\mathbf{x}^{\prime}(t)dt$ | https://www.youtube.com/watch?v=o7UCBjGsRTE | |
dy becomes y prime of t dt | $dy=y^{\prime}(t)dt$ | https://www.youtube.com/watch?v=o7UCBjGsRTE | |
the integral of f sub x times dx dt plus f sub y times dy dt | $\int f_{x}\frac{dx}{dt}+f_{y}\frac{dy}{dt}$ | https://www.youtube.com/watch?v=o7UCBjGsRTE | |
integral from t0 to t1 of dF dt dt | $\displaystyle \int_{t_{0}}^{t_{1}}\frac{dF}{dt}dt$ | https://www.youtube.com/watch?v=o7UCBjGsRTE | |
three y squared plus four x squared | $3y^{2}+4x^{2}$ | https://www.youtube.com/watch?v=z5TPjZrsp2k | |
four x squared plus eight xy | $4x^{2}+8xy$ | https://www.youtube.com/watch?v=z5TPjZrsp2k | |
four thirds x one cubed | $\frac{4}{3}x_{1}^{3}$ | https://www.youtube.com/watch?v=z5TPjZrsp2k | |
y cubed plus 4x1 squared y | $y^{3}+4x_1^{2}y$ | https://www.youtube.com/watch?v=z5TPjZrsp2k | |
f of x one and y one is four thirds x one cubed plus y one cubed plus four x one squared y one | $\displaystyle f(x_{1},y_{1})=\frac{4}{3}x_{1}^{3}+y_{1}^{3}+4x_{1}^{2}y_{1}$ | https://www.youtube.com/watch?v=z5TPjZrsp2k | |
4 x squared plus 8xy | $4x^{2}+8xy$ | https://www.youtube.com/watch?v=z5TPjZrsp2k | |
f sub y is three y squared plus four x squared | $f_{y}=3y^{2}+4x^{2}$ | https://www.youtube.com/watch?v=z5TPjZrsp2k | |
line integral along C of y e to the minus x dx plus one-half of x squared minus e to the minus x dy | $\displaystyle \oint_{C}({y}e^{-x})dx+(\frac{1}{2}x^{2}-e^{-x})dy$ | https://www.youtube.com/watch?v=tYdoS0tkAHA | |
x equals two plus cosine theta | $x=2+\cos\theta$ | https://www.youtube.com/watch?v=tYdoS0tkAHA | |
dx equals minus sine theta d theta | $dx=-\sin\theta d\theta$ | https://www.youtube.com/watch?v=tYdoS0tkAHA | |
Nx minus My dA | $\displaystyle (Nx - My)dA$ | https://www.youtube.com/watch?v=tYdoS0tkAHA | |
y equals f2 of x | $y =\mathcal{f}_{2}(x)$ | https://www.youtube.com/watch?v=tYdoS0tkAHA | |
integral from b to a of M of x and f2 of x dx | $\displaystyle \int_{b}^{a}M(x)(f_{2}(x))dx$ | https://www.youtube.com/watch?v=tYdoS0tkAHA | |
M of x f two of x minus M of x f one of x | $\displaystyle (M(x)f_{2}(x))-(M(x)f_{1}(x))$ | https://www.youtube.com/watch?v=tYdoS0tkAHA | |
square root of x squared plus y squared | $\sqrt{x^{2}+y^{2}}$ | https://www.youtube.com/watch?v=_CdoRiNSrqI | |
the double integral of P sub x plus Q sub y dA | $\iint(P_{x}+Q_{y})dA$ | https://www.youtube.com/watch?v=_CdoRiNSrqI | |
minus yi plus xj over x squared plus y squared | $\frac{-yi+{xj}}{x^{2}+y^{2}}$ | https://www.youtube.com/watch?v=PnPIqh7Frlw | |
u equals one plus t squared | $u=1+t^{2}$ | https://www.youtube.com/watch?v=PnPIqh7Frlw | |
the curl of f which is Nx minus My | $\displaystyle \operatorname{\nabla}\times F=Nx-My$ | https://www.youtube.com/watch?v=PnPIqh7Frlw | |
xy minus x squared | $xy-x^{2}$ | https://www.youtube.com/watch?v=PnPIqh7Frlw | |
z equals x squared plus y squared | $z=x^{2}+y^{2}$ | https://www.youtube.com/watch?v=44R5HgbrUmc | |
z equals four minus x squared minus y squared | $z=4-x^{2}-y^{2}$ | https://www.youtube.com/watch?v=44R5HgbrUmc | |
two x squared plus two y squared less than four | $2x^{2}+2y^{2}<4$ | https://www.youtube.com/watch?v=44R5HgbrUmc | |
y is square root of two minus x squared | $y=\sqrt{2-x^{2}}$ | https://www.youtube.com/watch?v=44R5HgbrUmc | |
plus minus root of two minus x squared | $\pm\sqrt{2-x^{2}}$ | https://www.youtube.com/watch?v=44R5HgbrUmc | |
x squared plus y squared plus z squared less than one | $x^{2}+y^{2}+z^{2}<1$ | https://www.youtube.com/watch?v=44R5HgbrUmc | |
z equals one minus y | $\displaystyle z=1-y$ | https://www.youtube.com/watch?v=44R5HgbrUmc | |
z equals square root of one minus x squared minus y squared | $z=\sqrt{1-x^{2}-y^{2}}$ | https://www.youtube.com/watch?v=44R5HgbrUmc | |
one minus y is less than square root of one minus x squared minus y squared | $1-y<\sqrt{1-x^{2}-y^{2}}$ | https://www.youtube.com/watch?v=44R5HgbrUmc | |
negative square root of two y minus two y squared | $-\sqrt{2y-2y^{2}}$ | https://www.youtube.com/watch?v=44R5HgbrUmc | |
rho times cosine phi | $\rho\cos \phi$ | https://www.youtube.com/watch?v=RMBGQtwkoyU | |
rho sine phi cos theta | $\rho\sin\phi\cos\theta$ | https://www.youtube.com/watch?v=RMBGQtwkoyU | |
rho sine phi sine theta. | $\rho\sin\phi\sin\theta$ | https://www.youtube.com/watch?v=RMBGQtwkoyU | |
z is rho cos phi | $z=\rho\cos\phi$ | https://www.youtube.com/watch?v=RMBGQtwkoyU | |
rho is the square root of r squared plus z squared | $\rho=\sqrt{r^{2}+z^{2}}$ | https://www.youtube.com/watch?v=RMBGQtwkoyU | |
phi equals pi over four | $\phi=\frac{\pi}{4}$ | https://www.youtube.com/watch?v=RMBGQtwkoyU | |
z equals r | $\mathcal{z}=\mathcal{r}$ | https://www.youtube.com/watch?v=RMBGQtwkoyU | |
a squared sine phi d phi d theta | $\displaystyle a^{2}\sin\phi d\phi d\theta$ | https://www.youtube.com/watch?v=RMBGQtwkoyU | |
rho squared sine phi d rho d phi d theta | $\rho^2\sin \phi d\rho d\phi d\theta$ | https://www.youtube.com/watch?v=RMBGQtwkoyU | |
z equals one over root two | $z=1/\sqrt{2}$ | https://www.youtube.com/watch?v=RMBGQtwkoyU | |
rho equals one over root two cosine phi | $\rho=\frac{1}{\sqrt{2}}\cos{\phi}$ | https://www.youtube.com/watch?v=RMBGQtwkoyU | |
one over root two times secant phi | $\frac{1}{\sqrt{2}}\cdot\sec\phi$ | https://www.youtube.com/watch?v=RMBGQtwkoyU | |
cos phi equals one over root two | $\cos\phi=\frac{1}{\sqrt{2}}$ | https://www.youtube.com/watch?v=RMBGQtwkoyU | |
phi equals pi over four | $\phi=\frac{\pi}{4}$ | https://www.youtube.com/watch?v=RMBGQtwkoyU | |
two pi over three minus five pi over six root two | $2\pi/3-5\pi/6\sqrt{2}$ | https://www.youtube.com/watch?v=RMBGQtwkoyU | |
rho cubed over three | $\rho^{3}/3$ | https://www.youtube.com/watch?v=RMBGQtwkoyU | |
sine phi secant cubed phi | $\sin\phi\sec^{3}\phi$ | https://www.youtube.com/watch?v=RMBGQtwkoyU | |
z over rho cubed delta dV | $\frac{z}{\rho^{3}}\Delta dV$ | https://www.youtube.com/watch?v=RMBGQtwkoyU | |
rho cosine phi over rho cubed | $\frac{\rho\cos\phi}{\rho^{3}}$ | https://www.youtube.com/watch?v=RMBGQtwkoyU | |
minus c times x y z over rho cubed | $-\frac{c(x,y,z)}{\rho^{3}}$ | https://www.youtube.com/watch?v=phk05iSMezA | |
xi yj zk | $\displaystyle xi+yj+zk$ | https://www.youtube.com/watch?v=phk05iSMezA | |
square root of x squared plus y squared plus z squared is equal to a | $\sqrt{x^{2}+y^{2}+z^{2}}=a$ | https://www.youtube.com/watch?v=phk05iSMezA | |
four pi a squared | $4\pi a^{2}$ | https://www.youtube.com/watch?v=phk05iSMezA | |
z squared over a | $\frac{\mathbb{z}^{2}}{a}$ | https://www.youtube.com/watch?v=phk05iSMezA | |
dS equals a squared sine phi d phi d theta | $dS=a^{2}\sin\phi d\phi d\theta$ | https://www.youtube.com/watch?v=phk05iSMezA | |
cosine squared phi sine phi d phi | $\cos^{2}\phi \sin\phi d\phi $ | https://www.youtube.com/watch?v=phk05iSMezA | |
four thirds pi a cubed | $\frac{4}{3}\pi a^{3}$ | https://www.youtube.com/watch?v=phk05iSMezA | |
f of x plus delta x and y | $f(x+\Delta x,y)$ | https://www.youtube.com/watch?v=WfEQabCGAqI | |
f of x, y plus delta x times f sub x | $f(x,y)+\Delta x\cdot f_{x}$ | https://www.youtube.com/watch?v=WfEQabCGAqI | |
f sub y times delta y | $\displaystyle f_y \times\Delta y$ | https://www.youtube.com/watch?v=WfEQabCGAqI | |
z equals x squared plus y squared | $z=x^{2}+y^{2}$ | https://www.youtube.com/watch?v=WfEQabCGAqI | |
partial r over partial u times delta u | $\displaystyle \frac{\partial r}{\partial u}\cdot\Delta u$ | https://www.youtube.com/watch?v=WfEQabCGAqI | |
z equals a cosine phi | $z=a\,\cos\phi$ | https://www.youtube.com/watch?v=WfEQabCGAqI | |
delta A equals delta S times the cosine of alpha | $\Delta A=\Delta S(\cos\alpha)$ | https://www.youtube.com/watch?v=WfEQabCGAqI | |
delta S is going to be one over cosine alpha | $\Delta S=\frac{1}{\cos\alpha}$ | https://www.youtube.com/watch?v=WfEQabCGAqI | |
three times little n will be negative big N | $3\mathrm{n}=\mathrm{-}\mathrm{N}$ | https://www.youtube.com/watch?v=WfEQabCGAqI | |
n over n dot i dy dz | $\displaystyle \frac{n}{n\cdot i}{dy}{dz}$ | https://www.youtube.com/watch?v=WfEQabCGAqI | |
z minus f of x y | $z-f(x,y)$ | https://www.youtube.com/watch?v=WfEQabCGAqI | |
P sub x plus Q sub y plus R sub z | $P_{x}+Q_{y}+R_{z}$ | https://www.youtube.com/watch?v=WfEQabCGAqI | |
four thirds pi a cubed | $\frac{4}{3}\pi a^{3}$ | https://www.youtube.com/watch?v=WfEQabCGAqI | |
partial u over partial x squared plus partial squared u over partial y squared plus partial squared u over partial z squared | $\displaystyle \frac{\partial u}{\partial x^{2}}+\frac{\partial^{2}u}{\partial y^ {2}}+\frac{\partial^{2}u}{\partial z^{2}}$ | https://www.youtube.com/watch?v=wu8kXZSAp20 | |
partial u partial t is minus div F, which is therefore positive k times divergence of grad u | $\displaystyle \frac{\partial\mathbf{u}}{\partial t}=\operatorname{-\nabla}\mathbf{F}=k\operatorname{\nabla}(\operatorname{\nabla}\mathbf{u})$ | https://www.youtube.com/watch?v=seO7-TwXH_I | |
dx is 3t2 dt | $dx=3t^{2}dt$ | https://www.youtube.com/watch?v=seO7-TwXH_I | |
dy will be 2t dt | $\displaystyle \mathrm{d}\mathrm{y}=2{t}{\mathrm{d}t}$ | https://www.youtube.com/watch?v=seO7-TwXH_I | |
the integral of yz dx plus xz dy plus xy dz | $\int yz\,dx+xz\,dy+xy\,dz$ | https://www.youtube.com/watch?v=seO7-TwXH_I | |
dx is 3t squared dt | $\displaystyle dx={3t}^{2}dt$ | https://www.youtube.com/watch?v=seO7-TwXH_I | |
xy is t to the five | $xy=t^{5}$ | https://www.youtube.com/watch?v=seO7-TwXH_I | |
six t to the five | $\displaystyle 6t^{5}$ | https://www.youtube.com/watch?v=seO7-TwXH_I | |
b y z squared minus 4z cubed | $byz^{2}-4z^{3}$ | https://www.youtube.com/watch?v=seO7-TwXH_I | |
x squared plus z cubed | $x^{2}+z^{3}$ | https://www.youtube.com/watch?v=seO7-TwXH_I | |
three yz squared minus four z cubed | $3yz^{2}-4z^{3}$ | https://www.youtube.com/watch?v=seO7-TwXH_I | |
f sub x is two xy | $f_{x}=2xy$ | https://www.youtube.com/watch?v=seO7-TwXH_I | |
f equals x squared y plus g | $f=x^{2}y+g$ | https://www.youtube.com/watch?v=seO7-TwXH_I | |
yz cubed plus h of z | $yz^{3}+h(z)$ | https://www.youtube.com/watch?v=seO7-TwXH_I | |
zero plus three yz squared | $0+3yz^{2}$ | https://www.youtube.com/watch?v=seO7-TwXH_I |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.