Fundamental Theorem of Calculus Proof

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 $[1,4]$

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

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