Finding the Area Under the Curve

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

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

Prove the fundamental theorem of calculus