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

Check your work by differentiating your answer. Make sure the coefficients are correct.

3. $\int _ { 1 } ^ { 2 } x ^ { x } d x$

In this course, you will discover strategies to differentiate (and integrate) exponential functions. But you have not discovered this process yet. Use your calculator.

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 $x = 5$.