6)Find the indefinite integral :cos ( TX ) dxsin³ ( Tx )

The given integral is , ∫cosπxsin3πxdx Substitute u→sinπx. dudx=πcosπx dx=1πcosπxdu Therefore the…

Answered: Find the indefir COS cos ( TX ) di 3

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter1: Systems Of Linear Equations

Section1.3: Applications Of Systems Of Linear Equations

Problem 13E: Use sin0=0, sin2=1, and sin=0 to estimate sin3.

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Question

6)
Find the indefinite integral :
cos ( TX ) dx
sin³ ( Tx )

Expert Solution

Step 1

The given integral is , $\int \frac{\cos (π x)}{\sin^{3} (π x)} d x$

Substitute $u \to \sin (π x) .$

$\frac{d u}{d x} = π \cos (π x)$

$d x = \frac{1}{π \cos (π x)} d u$

Therefore the integral becomes,

$\frac{1}{π} \int \frac{d u}{u^{3}} = \frac{1}{π} [\frac{- 1}{2 u^{2}}]$

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