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Math 152 metric IHU 3. In this problem we'll evaluate the integral cos²(z) sin³ (2) dr. (a) First, we'll re-write sin³ (2) as sin²(x) sin(r). Write the integral with this change made. (b) Now, we'll convert sin²(z) to an expression that involves cosine instead. Use the identity sin² 0 + cos² 0 = 1 to replace sin2 (r) with something involving cosines, and w the integral with the change made. (c) At this point we can use a u-substitution to make this integral much easier. Substitute U= cos(x). Write the new integral completely in terms of u. (d) Distribute any multiplication inside your integral, then integrate and complete the integral.

Math 152 metric IHU 3. In this problem we'll evaluate the integral cos²(z) sin³ (2) dr. (a) First, we'll re-write sin³ (2) as sin²(x) sin(r). Write the integral with this change made. (b) Now, we'll convert sin²(z) to an expression that involves cosine instead. Use the identity sin² 0 + cos² 0 = 1 to replace sin2 (r) with something involving cosines, and w the integral with the change made. (c) At this point we can use a u-substitution to make this integral much easier. Substitute U= cos(x). Write the new integral completely in terms of u. (d) Distribute any multiplication inside your integral, then integrate and complete the integral.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 70E
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Math 152 ometric Int 3. In this problem we'll evaluate the integral cos²(z) sin³(x) dx. (a) First, we'll re-write sin³ (2) as sin² (2)- sin(x). Write the integral with this change made. (b) Now, we'll convert sin² (r) to an expression that involves cosine instead. Use the identity sin²0 + cos²0 = 1 to replace sin² (2) with something involving cosines, and w the integral with the change made. (c) At this point we can use a u-substitution to make this integral much easier. Substitute U= cos(x). Write the new integral completely in terms of u. (d) Distribute any multiplication inside your integral, then integrate and complete the integral.
Transcribed Image Text:Math 152 ometric Int 3. In this problem we'll evaluate the integral cos²(z) sin³(x) dx. (a) First, we'll re-write sin³ (2) as sin² (2)- sin(x). Write the integral with this change made. (b) Now, we'll convert sin² (r) to an expression that involves cosine instead. Use the identity sin²0 + cos²0 = 1 to replace sin² (2) with something involving cosines, and w the integral with the change made. (c) At this point we can use a u-substitution to make this integral much easier. Substitute U= cos(x). Write the new integral completely in terms of u. (d) Distribute any multiplication inside your integral, then integrate and complete the integral.
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