# Math Help - testing

1. ## definate integrals.--please help.

please could someone solve the following definate integrals. help will be much appreciated.

A)
$
\int_0^{\pi^2} \left(\sin 4\theta - \cos 4\theta\right)^2d\theta
$

Note: the pi is supposed to be pi over 2 rather than squared.

B)
$
\int_1^2(15x^3+e^2x-\frac{4}{x})dx
$

2. Originally Posted by Diane Charlton
$
\int_0^{\pi^2} \left(\sin 4\theta - \cos 4\theta\right)^2d\theta
$

Note: the pi is supposed to be pi over 2 rather than squared.
Then you mean
$\int_0^{\pi/2} ( sin(4 \theta) - cos(4 \theta))^2~d\theta$

$= \int_0^{\pi/2} ( sin^2(4 \theta) - 2sin(4 \theta)~cos(4 \theta) + cos^2(4 \theta) )~d\theta$

$= \int_0^{\pi/2} ( 1 - 2sin(4 \theta)~cos(4 \theta))~d\theta$

$= \int_0^{\pi/2} ( 1 - sin(8 \theta))~d\theta$

Which I'm sure you can do easily now.

-Dan