Given ${\int }_0^{3}p(x)dx=-8$, find ${\int }_3^{0}p(x)dx$.

If $\frac{dy}{dx}=6x^2+8$ and $y(3)=-2$, find $y$ as a function of $x$.

Evaluate $\int \frac{-8}{x}dx$.

If $G(x)={\int }_2^{2x}\left(t^2-6\right)dt$, find $G^{\prime }\left(4\right)$.

Find $\int \frac{4x^3}{x^4+6}dx$.

Evaluate $\int \left(-2x^3+7\right)dx$.

Given ${\int }_0^{3}f(x)dx=-2$ and ${\int }_0^{6}f(x)dx=5$, find ${\int }_3^{6}f(x)dx$.

Find the area of the region bounded by $y=x^3$, the $x$-axis, $x=0$ and $x=5$.

If $G(x)={\int }_3^{x^3}\sin tdt$, find $G^{\prime }\left(x\right)$.

Solve $\frac{dy}{dx}=10xy$ with $y(0)=6$, giving $y$ explicitly.

A bacteria culture grows continuously and doubles every $6$ hours. If it starts at $800$ cells, how many cells are there after $24$ hours?

Find $\int {\cos }^{3}x\sin xdx$, with $x$ in radians.

Given ${\int }_1^{6}f(x)dx=3$ and ${\int }_1^{6}h(x)dx=-1$, find ${\int }_1^6\left(3f(x)-2h(x)\right)dx$.

Evaluate ${\int }_0^{1}x{\left(x^2+5\right)}^{2}dx$.

A particle moves along a line with velocity $v(t)=t^2-6t$ meters per second, for $0\le t\le 10$. Find the TOTAL DISTANCE it travels over that interval.

A crowd enters a stadium at a rate of $P(t)=8t-t^2$ people per minute, for $0\le t\le 1$. What is the total change in the number of people over that $1$ minute?

Approximate ${\int }_0^{4}3x^{2}dx$ with the TRAPEZOIDAL rule using $4$ equal subintervals.

Approximate ${\int }_1^{5}4x^{2}dx$ with a RIGHT Riemann sum using $4$ equal subintervals.

The region between $y=2x$ and $y=2x^2$ is revolved about the $x$-axis. What is the volume?

Evaluate ${\int }_0^3\left(-3x+7\right)dx$.

Find $\int x{\left(x^2+1\right)}^{2}dx$.

Sand pours onto a pile, at rate $S$ in kilograms per second, with $t$ in seconds: $S(0)=2$, $S(2)=5$, $S(7)=9$, $S(11)=14$. Use a LEFT Riemann sum with the table's three subintervals to approximate the total, in kilograms.

Find the general solution of $\frac{dy}{dx}=\frac{3x^5}{y}$ in IMPLICIT form.

If $g(x)={\int }_x^5\sqrt{t^3+1}dt$, find $g^{\prime }\left(x\right)$.

A particle moves along a line with velocity $v(t)=t^2-4t$ meters per second, for $0\le t\le 8$. Find the particle's DISPLACEMENT over that interval.

What is the average value of $f(x)=5e^x$ on $\left[0,3\right]$?

The base of a solid is the region bounded by $y=\sqrt{4x}$, the $x$-axis and $x=6$. Cross sections perpendicular to the $x$-axis are SQUARES with one side in the base. What is the volume?

A radioactive sample decays continuously with a half-life of $30$ days. What is $k$ in $y=y_0{e}^{kt}$, with $t$ in days?

Evaluate ${\int }_2^3\left(-5x+6\right)dx$.

Evaluate ${\int }_0^3{e}^{x}dx$.

The region is bounded by $y=\sqrt{x}$, the $y$-axis, $y=3$ and $y=6$, with $x\ge 0$. Which integral gives its area in HORIZONTAL strips?

Find the area of the region enclosed by $y=-7x-12$ and $y=x^2$.

Given ${\int }_0^{3}h(x)dx=-4$ and ${\int }_0^{6}h(x)dx=-3$, find ${\int }_3^{6}h(x)dx$.

Evaluate $\int \left(2x^7-8\right)dx$.

A particle moves along a line with velocity $v(t)=t^2-4t$ meters per second, for $0\le t\le 5$. Find the TOTAL DISTANCE it travels over that interval.

The region between $y=6x$ and $y=2x^2$ is revolved about the $x$-axis. What is the volume?

Find the area of the region bounded by $y=x^2+1$, the $x$-axis, $x=0$ and $x=5$.

Given ${\int }_4^{7}g(x)dx=-2$, find ${\int }_7^{4}g(x)dx$.

Oil leaks from a drum at a rate of $L(t)=4t-t^2$ liters per minute, for $0\le t\le 3$. How much oil leaks out over those $3$ minutes?

If $G(x)={\int }_2^{x^2}{e}^{t^2}dt$, find $G^{\prime }\left(x\right)$.