### Home > APCALC > Chapter 4 > Lesson 4.4.2 > Problem4-146

4-146.

Examine the integrals below. Consider the multiple tools available for evaluating integrals and use the best strategy for each part. Evaluate the definite integrals and state the strategies that you used. For the indefinite integrals, find the antiderivative function, if you can.

1. $\int \sqrt { 1 - x ^ { 4 } } d x$

2. $\int ( \frac { 4 } { m ^ { 3 } } - 3 \operatorname { cos } ( m ) ) d m$

3. $\int _ { 1 } ^ { 2 } x ^ { x } d x$
4. $\int \pi ^ { 2 } d x$
Consider what the graph of $\pi^2$ looks like. Is its area function linear or quadratic?
5. $\int _ { 0 } ^ { 5 } ( | x - 2 | + 3 ) d x$
To avoid rewriting the integrand as a piecewise function, you could sketch the graph and geometrically compute the area between $x = 0$ and $x = 5$.