Trigonometric Substitution Question

**Troopa** · January 21st 2010, 08:24 PM

Hello,

I am absolutely stumped on this one.

I'm assuming all of my work is correct up until the end, but I don't know how to proceed using Trigonometric Substitution. Please help!

**Jhevon** · January 21st 2010, 08:37 PM

Originally Posted by Troopa

Hello,

I am absolutely stumped on this one.

I'm assuming all of my work is correct up until the end, but I don't know how to proceed using Trigonometric Substitution. Please help!

$\frac 1{\sec^2 \theta} = \cos^2 \theta = \frac 12 (1 + \cos 2 \theta)$

(and of course it's not $\frac 1{\tan \theta + C}$ there is no integration rule to justify such a step!)

**Troopa** · January 21st 2010, 08:52 PM

So then...

$= \frac 12 (1 + \cos 2 \theta)$

$= \frac 12 (\theta + (cos2 \theta^2 / 2))$

Is this right?

**Jhevon** · January 21st 2010, 08:54 PM

Originally Posted by Troopa

So then...

$= \frac 12 (1 + \cos 2 \theta)$

$= \frac 12 (\theta + (cos2 \theta^2 / 2))$

Is this right?

no.

first, where's your integral sign?

secondly, how do we integrate cosine? We don't just simply integrate the argument.

**VonNemo19** · January 21st 2010, 09:03 PM

$\int\frac{1}{\sec^2\theta}d\theta=\int\cos^2\theta {d}\theta=\frac{1}{2}\int(1+\cos2\theta)d\theta=\f rac{1}{2}(\theta+\frac{1}{2}\sin{2\theta})+C$

Now back substitute.

**Troopa** · January 21st 2010, 09:06 PM

Thanks for your help. I'm gonna finish this and get some help in my math lab.

Thread: Trigonometric Substitution Question

LinkBack

Thread Tools

Display

Trigonometric Substitution Question

Similar Math Help Forum Discussions

Trigonometric substitution.

trigonometric substitution

Trigonometric substitution

trigonometric substitution

Trigonometric substitution?

Search Tags