Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![### Integral Evaluations
You know that:
- \(\int_{1}^{3} g(t) \, dt = 16\)
- \(g(1) = 1\)
- \(g(3) = 4\)
#### a) Evaluate:
\[
\int_{1}^{3} \frac{g'(x)}{\sqrt[3]{5 + 4g(x)}} \, dx = \boxed{\frac{1}{6} \left( 21^{ \frac{3}{2} } - 9^{ \frac{3}{2} } \right)}
\]
#### b) Evaluate:
\[
\int_{ \frac{1}{16} }^{ \frac{9}{16} } g(4\sqrt{x}) \, \frac{1}{\sqrt{x}} \, dx = \boxed{}
\]
---
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Transcribed Image Text:### Integral Evaluations
You know that:
- \(\int_{1}^{3} g(t) \, dt = 16\)
- \(g(1) = 1\)
- \(g(3) = 4\)
#### a) Evaluate:
\[
\int_{1}^{3} \frac{g'(x)}{\sqrt[3]{5 + 4g(x)}} \, dx = \boxed{\frac{1}{6} \left( 21^{ \frac{3}{2} } - 9^{ \frac{3}{2} } \right)}
\]
#### b) Evaluate:
\[
\int_{ \frac{1}{16} }^{ \frac{9}{16} } g(4\sqrt{x}) \, \frac{1}{\sqrt{x}} \, dx = \boxed{}
\]
---
Upload your handwritten work in the box below:
Make sure to show the entire process of evaluating these integrals.
Report **EXACT** answers.
Use correct notation.
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I dont understand what you have done in at the beggining. How di you change the limits?
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