Need help

Moistwh

New member
Joined
Mar 16, 2019
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1
How should i evaluate the following integral? 11396

My teacher told me to use x = sec(t)/6 as an inverse trig substitution, but i end up with (secx)^3/216(tanx) and do not know how to proceed
Any hints?
 

MarkFL

Super Moderator
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Joined
Nov 24, 2012
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994
Okay, using the suggested substitution:

\(\displaystyle x=\frac{\sec(t)}{6}\implies dx=\frac{1}{6}\sec(t)\tan(t)\,dt\)

We then get:

\(\displaystyle I=\frac{1}{6^4}\int_0^{\frac{\pi}{4}} \sec^4(t)\,dt\)

Can you proceed?
 
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