Definite Integral Practice Problems

Evaluate the following definite integral

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

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

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

Find the area under the curve over the interval $[1,4]$

$f(x) = \frac{2}{x}$

Find the area the region bounded by:

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

$x = 0$

$x = 8$

$y = 0$