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##