Calculus 1

Find the area under the curve over the interval $[0,4]$

$f(x) = x^2 + 1$

Evaluate the integral $\displaystyle\int_{\frac{\pi}{4}}^{\frac{\pi}{2}} (2 - \csc^2{x}) \ dx$

Find the area the region bounded by:

$y = 1 + \sqrt[3]{x}$

$x = 0$

$x = 8$

$y = 0$

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

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 of the solid formed by rotating the region about the y axis.

$y = x^2 + 2$

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