AP Calculus AB Unit 8: Applications of Integration

Use the washer method to find the volume when the region between $y=x$ and $y=x^2$ (on $[0,1]$) is rotated about the $x$-axis.

A particle's velocity is $v(t)=t^2-4t+3$ for $0\le t\le 4$. What is the total distance traveled?

Find the area enclosed between $y=x$ and $y=x^2$ on $[0,1]$.

Find the volume of the solid with square cross-sections perpendicular to the $x$-axis, where the base is the region bounded by $y=\sqrt{x}$ and $y=0$ on $[0,4]$.

What is the average value of $f(x)=4x$ on $[1,3]$?

Find the area between $y=\sin x$ and $y=\cos x$ on $\left[\frac{\pi }{4},\frac{5\pi }{4}\right]$.

Find the volume of the solid formed when the region bounded by $y=e^x$, the $x$-axis, $x=0$, and $x=1$ is rotated about the $x$-axis.

A particle moves along the $x$-axis with velocity $v(t)=t^2-4$ for $0\le t\le 3$. What is the total displacement?

The acceleration of a particle is $a(t)=6t$ with $v(0)=-2$ and $s(0)=4$. Find $s(3)$.

Using the disk method, find the volume of the solid formed by rotating $y=\sqrt{x}$ on $[0,4]$ about the $x$-axis.

Find the area between $y=x^2$ and the $x$-axis on $[0,3]$.

A tank contains $100$ gallons of water. Water drains at rate $r(t)=5t$ gal/min. How much water drains out in the first $4$ minutes?