M Moistwh New member Joined Mar 16, 2019 Messages 1 Saturday at 10:02 PM #1 How should i evaluate the following integral? 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?

How should i evaluate the following integral? 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 Staff member Joined Nov 24, 2012 Messages 994 Saturday at 10:19 PM #2 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?

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?