Calculus 1

$\int{\frac{8}{9+r^2}}dr$

Find $\displaystyle\int\frac{2x}{1 + 2x^2} \ dx$

Evaluate $\displaystyle\int\frac{e^{ \ p \ \tan^{-1}(x)}}{1 + x^2} \ dx$

Evaluate the definite integral below

$\displaystyle\int_{-2}^2 \ {x^2 \cos{(\frac{x^3}{8})}} \ dx$

Evaluate the following definite integral

$\displaystyle\int_0^4 \ x \sqrt{x^2 + 9} \ dx$

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.

$y = x^2 + 2$

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