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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![### Calculus Exercises
4. **Find the area bounded by the curves:**
\( f(x) = x^2 \) and \( f(x) = x^3 \).
You have to find the limits of integration by graphing or solving.
5. **Given that:**
\[
\int_{0}^{3} x^2 \, dx = 9
\]
Evaluate:
\[
\int_{0}^{3} (x^3 - 4x^2) \, dx
\]
Now evaluate:
\[
\int_{3}^{0} -4x^2 \, dx
\]
6. **If:**
\[
\int_{0}^{1} x^2 \, dx = \frac{1}{3} \quad \text{and} \quad \int_{0}^{3} x^2 = 9
\]
Find:
\[
\int_{1}^{3} x^2 \, dx
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F97689b57-22f1-451b-aeb3-e5f10664de40%2F6296e9c6-fb16-4d4b-ab69-bf7a21e35683%2Ftaee1gq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Calculus Exercises
4. **Find the area bounded by the curves:**
\( f(x) = x^2 \) and \( f(x) = x^3 \).
You have to find the limits of integration by graphing or solving.
5. **Given that:**
\[
\int_{0}^{3} x^2 \, dx = 9
\]
Evaluate:
\[
\int_{0}^{3} (x^3 - 4x^2) \, dx
\]
Now evaluate:
\[
\int_{3}^{0} -4x^2 \, dx
\]
6. **If:**
\[
\int_{0}^{1} x^2 \, dx = \frac{1}{3} \quad \text{and} \quad \int_{0}^{3} x^2 = 9
\]
Find:
\[
\int_{1}^{3} x^2 \, dx
\]
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