Approximate ${\int }_1^{5}4x^{2}dx$ with the TRAPEZOIDAL rule using $4$ equal subintervals.

Evaluate $\int \left(4x^5-3\right)dx$.

Traffic passes a sensor, at rate $N$ in cars per minute, with $t$ in minutes: $N(0)=4$, $N(3)=7$, $N(6)=11$, $N(10)=16$. Use a LEFT Riemann sum with the table's three subintervals to approximate the total, in cars.

Evaluate $\int e^{4x}dx$.

Water enters a tank at a rate of $r(t)=9t-t^2$ gallons per hour, for $0\le t\le 2$. What is the total change over those $2$ hours?

Evaluate $\int -9x^{-4}dx$.

Given ${\int }_0^{5}p(x)dx=3$ and ${\int }_0^{8}p(x)dx=6$, find ${\int }_5^{8}p(x)dx$.

If $H(x)={\int }_1^{e^x}\ln \left(t^2+1\right)dt$, find $H^{\prime }\left(x\right)$.

Approximate ${\int }_3^{5}2x^{2}dx$ with a RIGHT Riemann sum using $2$ equal subintervals.

Evaluate $\int 5\sin xdx$, with $x$ in radians.

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

A function is continuous and DECREASING on $\left[0,6\right]$. Is a LEFT Riemann sum an over-estimate or an under-estimate of ${\int }_0^{6}f(x)dx$?

Evaluate $\int e^{5x}dx$.

Find $\int x{\left(x^2+8\right)}^{2}dx$.

If $G(x)={\int }_1^{x^2}\sin tdt$, find $G^{\prime }\left(x\right)$.

A function has $q^{\prime }\left(x\right)=-5x$ and $q(-4)=9$. What is the constant of integration in $q(x)=-\frac{5}{2}{x}^2+C$?

If $p(x)={\int }_1^{x^3}{e}^{t^2}dt$, find $p^{\prime }\left(x\right)$.

Find $\int {\tan }^{6}x{\sec }^{2}xdx$, with $x$ in radians.

Given ${\int }_0^{5}h(x)dx=-2$ and ${\int }_0^{8}h(x)dx=1$, find ${\int }_5^{8}h(x)dx$.

Approximate ${\int }_0^{4}3x^{2}dx$ with a RIGHT Riemann sum using $2$ equal subintervals.

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

Evaluate $\int \left(x^4+9\right)dx$.

The figure shows the graph of $f$. Let $G(x)={\int }_0^{x}f(t)dt$. Find $G(4)$.

Evaluate $\int \left(5x^4+1\right)dx$.

Find $\int {\sin }^{4}x\cos xdx$, with $x$ in radians.

A particle moves along a line with velocity $v(t)=t^2-6t$ meters per second, for $0\le t\le 7$. Find the TOTAL DISTANCE it travels over that interval.

Evaluate ${\int }_0^{2}x{\left(x^2+2\right)}^{3}dx$.

A function has $f^{\prime }\left(x\right)=-2x^3$ and $f(-6)=-5$. What is the constant of integration in $f(x)=-\frac{1}{2}{x}^4+C$?

Evaluate ${\int }_0^{\frac{\pi }{4}}{\sec }^{2}xdx$, with $x$ in radians.

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

Evaluate $\int -2x^{-6}dx$.

Given ${\int }_0^{5}p(x)dx=8$ and ${\int }_0^{8}p(x)dx=5$, find ${\int }_5^{8}p(x)dx$.

The figure shows the graph of $f$. Let $q(x)={\int }_0^{x}f(t)dt$. Find $q(2)$.

Evaluate ${\int }_0^{1}x{\left(x^2+3\right)}^{3}dx$.

A colony grows, at rate $B$ in bacteria per hour, with $t$ in hours: $B(0)=6$, $B(2)=9$, $B(5)=13$, $B(9)=18$. Use a LEFT Riemann sum with the table's three subintervals to approximate the total, in bacteria.

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

Evaluate $\int e^{9x}dx$.

A function has $q^{\prime }\left(x\right)=-6x^3$ and $q(6)=-1$. What is the constant of integration in $q(x)=-\frac{3}{2}{x}^4+C$?

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

If $H(x)={\int }_1^{4x}\cos \left(t^2\right)dt$, find $H^{\prime }\left(x\right)$.