#31 CalcChat.com for tutorial help and worked-out solutions to oClnCln 5et30.29.1 + e2xInn findu havesin x32.31.1/2dx1 + cos? xarcsin xdx34.33.V1- xwords,Completing the Squafind or evaluate the inte of asquaresquare.dxExercises35.36.x2 - 2x + 237.dx

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Answered: sin x dx 1+ cos2 x 31. T/2

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Calculus

sin x dx 1+ cos2 x 31. T/2

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter1: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 40RE

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Question

#31

CalcChat.com for tutorial help and worked-out solutions to o
Cln
Cln 5
et
30.
29.
1 + e2x
In
n find
u have
sin x
32.
31.
1/2
dx
1 + cos? x
arcsin x
dx
34.
33.
V1- x
words,
Completing the Squa
find or evaluate the int
e of a
square
square.
dx
Exercises
35.
36.
x2 - 2x + 2
37.
dx

Expert Solution

Step 1

NOTE: Refresh your page if you can't see any equations.

$\int _{\frac{\pi }{2}}^{\pi }\frac{\sin \left(x\right)}{1+\cos ^2\left(x\right)}dx\:$ ................(1)

substitute

$u=\cos \left(x\right)$

$\:du=-\sin \left(x\right)dx$

$\:\frac{du}{-\sin \left(x\right)}=dx$

$dx=\:-\frac{du}{\sin \left(x\right)}$ ................put it back in equation 1

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