# A) Evaluate the integral: integral of (x + 4)/(x^2 + 4) dx. B) Evaluate the integral: integral...

## Question:

A) Evaluate the integral: {eq}\int \frac{x + 4}{x^2 + 4} \, \mathrm{d}x {/eq}.

B) Evaluate the integral: {eq}\int_{0}^{\frac{\pi}{2}} \sqrt{1 - \cos \theta} \; \mathrm{d} \theta {/eq}.

## Techniques for Integrals:

Evaluating integrals sometimes require recognizing familiar forms of derivatives of known functions. Will a substitution work? If it's close, maybe there is something we can do to make it so that a substitution works. Or maybe we can expand the integrand to make integration easier. Identities and simplifying the integrand might also work. All techniques we have can solve a lot of different integrals, and combinations of them even more.

(A) For the integral $$\int \frac{x + 4}{x^2 + 4} \, \mathrm{d}x$$ we can divide each term and get \int \frac{x + 4}{x^2 + 4} \, \mathrm{d}x =...