sub u w/ trig?

**delgeezee** · December 4th 2011, 08:50 PM

I have been getting better but I am having trouble with this evil integral.

Evalute the following integrel:

$\int_{}{} sin^2(3x+\frac{\pi}{8}) dx$

The answer is = $\frac{x}{2}- \frac{1}{12}sin(6x+\frac{\pi}{4})+c$

Here was my first path of deduction

$\int_{}{} sin^2(3x+\frac{\pi}{8}) dx$ ; $u=3x+\frac{\pi}{8}$ , $u'=3$

dx in terms of u: $1dx=3du \Rightarrow du=\frac{1}{3}$

$\int_{}{} sin^2(u) \frac{1}{3}du$ = $\frac{1}{3} \int_{}{} sin^2(u)du$ = $\frac{1}{3} \int_{}{} (sinu)^2du$

I am stuck here. I can't directly integrate anything.

**Prove It** · December 4th 2011, 09:08 PM

Originally Posted by delgeezee

I have been getting better but I am having trouble with this evil integral.

Evalute the folling integrel:

$\int_{}{} sin^2(3x+\frac{\pi}{8}) dx$

Here was my first path of deduction

$\int_{}{} sin^2(3x+\frac{\pi}{8}) dx$ ; $u=3x+\frac{\pi}{8}$ , $u'=3$

dx in terms of u: $1dx=3du \Rightarrow du=\frac{1}{3}$

$\int_{}{} sin^2(u) \frac{1}{3}du$ = $\frac{1}{3} \int_{}{} sin^2(u)du$ = $\frac{1}{3} \int_{}{} (sinu)^2du$

I am stuck here. I can't directly integrate anything.

Hint: $\displaystyle \begin{align*} \sin^2{x} \equiv \frac{1}{2} - \frac{1}{2}\cos{2x} \end{align*}$

Math Help - sub u w/ trig?

LinkBack

Thread Tools

Display

sub u w/ trig?

Re: sub u w/ trig?

Similar Math Help Forum Discussions

Compute Trig Function Values, Solve Trig Equation

Trig word problem - solving a trig equation.

A few trig problems- help please (double angle and simplifying trig expressions)

Trig ratios, other trig mapping questions :/ Help greatly appreciated

Can someone check my Trig (Trig Form and Demoive's Theorm