### Home > CALC > Chapter 4 > Lesson 4.2.4 > Problem4-87

4-87.

Evaluate the following integrals.

1. $\int ( 6 x ^ { 3 } - 2 x + 5 ) d x$

'Undo' the Power Rule.

2. $\int _ { 2 } ^ { 4 } ( 6 x ^ { 3 } - 2 x + 5 ) d x$

Use your answer from part (a) to compute the integral on the interval from $2$ to $4$.

$358$

3. $\int ( 9 t ^ { 2 } - 1 ) d t$

See the hint from part (a).

4. $\int _ { - 2 } ^ { 2 } ( 9 t ^ { 2 } - 1 ) d t$

Use your answer from part (c) to compute the integral on the interval from $−2$ to $2$.

5. $\int ( \operatorname { sin } m + \frac { 1 } { 3 } m ^ { 2 } ) d m$

Remember that the integral of $\operatorname{sin}(x)$ is $-\operatorname{cos}(x) + C$.

6. $\int _ { - \pi } ^ { \pi } ( \operatorname { sin } m + \frac { 1 } { 3 } m ^ { 2 } ) d m$

Use your answer from part (e) to compute the integral on the interval from $−π$ to $π$

$\frac{2\pi ^3}{9}$
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