## Calculus 8th Edition

Published by Cengage

# Chapter 4 - Integrals - 4.4 Indefinite Integrals and the Net Change Theorem - 4.4 Exercises - Page 337: 47

#### Answer

The change in the child’s weight (in pounds) between the ages of 5 and 10

#### Work Step by Step

The problem states that $w'(t)$ is the rate of growth of a child in pounds every year. This makes $w(t)$ the amount of pounds that the child grew by. In this case, the integral $\int_5^{10} w'(t) dw$ looks at the years $5$ and $10$ of the child's growth. Since $\int w'(t) dw = w(t)$, $\int_5^{10} w'(t) = w(10) - w(5)$ by the formula $$\int_a^b w'(t) = w(b) - w(a)$$ Therefore, we get the change in the child’s weight (in pounds) between the ages of 5 and 10

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