Chapter 4 - Integrals - 4.4 Indefinite Integrals and the Net Change Theorem - 4.4 Exercises - Page 337: 25

$8$

When integrating the two trigonometric terms, we can ignore the constants $4$ and $3$ when evaluating the terms and rewrite the proven as $4\int sin \theta d \theta - 3\int cos \theta d \theta$ These integrals evaluate to $-4cos \theta - 3 sin \theta $ We now substitute $0$ and $\pi$ to $\theta$, which gives us the difference $(-4cos\pi - 3sin\pi) - (-4cos(0) - 3sin(0)) $ $= (-4(-1) - 0) - ((-4)(1) - 0)) = (4) - (-4) = 8 $