Step 4 Thus, (x x cos(8x) dx =

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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Please answer only the step 4
Step 2
To find the integral x cos 8x dx by the parts formula, use u = x and v =
1
sin 8x, as used in the previous step.
8
Apply the rule of integration by parts.
Judv
u dv = uv -
V
du
V
Step 3
Substitute the expressions for u and v in the integral.
J
x cos 8x dx = x
(si
sin(
✓
8 x) -
//=/
8 x) dx
Apply the constant multiplication rule to integrate the right side and simplify.
X
√x cos
x cos 8x dx =
sin 8x - (-¹cos Bx) + C
1
64
Step 4
Thus,
x
x cos(8x) dx =
8
8
x sin 8x +
64
sin(
cos 8x + C
Transcribed Image Text:Step 2 To find the integral x cos 8x dx by the parts formula, use u = x and v = 1 sin 8x, as used in the previous step. 8 Apply the rule of integration by parts. Judv u dv = uv - V du V Step 3 Substitute the expressions for u and v in the integral. J x cos 8x dx = x (si sin( ✓ 8 x) - //=/ 8 x) dx Apply the constant multiplication rule to integrate the right side and simplify. X √x cos x cos 8x dx = sin 8x - (-¹cos Bx) + C 1 64 Step 4 Thus, x x cos(8x) dx = 8 8 x sin 8x + 64 sin( cos 8x + C
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