# Calculus 1: Applications of Integration

Find the area between the two curves $y = x^4 - 2x^2$ and $y = 2x^2$

Find the area bounded by the following curves/lines

$y = x + 1$

$y = 9 - x^2$

$x = -1$

$x = 2$

Find the area between the curves $y = x$ and $y = x^2$

Compute the area between $y = \sin{x}$ and $y = \cos{x}$ and the interval $[\frac{\pi}{4}, \frac{5\pi}{4}]$

Compute the area of the region bounded by the curves $y = x^3$ and $y = 3x - 2$

Find the average value on $[0, 16]$ of $f(x) = \sqrt{x}$

What is the average value of the function $f(x) = 3x^2 - 2x$ on $[1, 4]$

Find the average value of the function $h(x) = \cos^4{(x)}\sin(x)$ on $[0, \pi]$

Determine the volume of the solid generated by rotating the function about the x-axis on $[0,3]$

$y = \sqrt{9 - x^2}$

Determine the volume of the solid generated by rotating the function about the y-axis on $[0,4]$

$y = \sqrt{x}$

Use the shell method to determine the volume formed by the bounded region rotated about the x-axis.

$y = x^2$, $y = 0$, $x = 2$

Use the shell method to determine the volume of the solid formed by rotating the region about the y axis.

$y = x^2 + 2$

$y = 0$, $x = 0$, $x = 2$

Use the disk method to find the volume of the solid of rotation by rotating the bounded area around the y-axis

$y = 2x^2$, $y = 0$, $x = 2$