Definite Integration

Evaluate the definite integral below

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

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 $[1,4]$

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

Evaluate the integral

$\displaystyle\int_0^2 (2x - 2x^2) \ dx$