9. 2x dx Vx2 + 64

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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Evaluate the definite integral. Use the integration capabilities of a graphing utility to verify your result.
2x
dx
+ 64
Vx2 +
Step 1
6.
2x
dx, apply the basic integration rule.
64
To find the definite integral
2 x dx.
Let u = x2
+ 64. Differentiate u in terms of x, du = 64 X
Step 2
Rewrite the integration in terms of u.
x6 2 X
1
du
9.
2x
| + 64
dx =
Step 3
Apply the power rule of integration.
1
du
du
%D
+ 1
1x = 6
%3D
+ 1Jo
X = 6
%3D
Transcribed Image Text:Evaluate the definite integral. Use the integration capabilities of a graphing utility to verify your result. 2x dx + 64 Vx2 + Step 1 6. 2x dx, apply the basic integration rule. 64 To find the definite integral 2 x dx. Let u = x2 + 64. Differentiate u in terms of x, du = 64 X Step 2 Rewrite the integration in terms of u. x6 2 X 1 du 9. 2x | + 64 dx = Step 3 Apply the power rule of integration. 1 du du %D + 1 1x = 6 %3D + 1Jo X = 6 %3D
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