Math Help Forum - View Single Post

AfterShock · #16 September 19th, 2007, 05:40 PM

Quote:

Originally Posted by taurus

I got another question:
Find the simplest function g(q) such that

g'(q) = sin( 5 q) +cos( 5 q)

im not sure how i should go about solving it?

First off, please place new questions in a new thread.

By finding the "integral," you're finding the "antiderivative."

$\int g'(q)\, dq = \int [\sin(5q) + \cos(5q)]\,dq = \int \sin(5q)\, dq + \int \cos(5q)\, dq = g(q)$

And thus,

$\int \sin(5q)\, dq + \int \cos(5q)\, dq = \frac{\sin(5q)}{5} - \frac{\cos(5q)}{5} + C$

We find this by, for example, letting $q = 5q$ then, $du = 5\, dq \Rightarrow \frac{1}{5} du = 5$ and thus for the first integral we have $\int \sin(5q)\, dq = \frac{1}{5}\cdot \int \sin(u)\, du = \frac{1}{5}\cdot -\cos(u) + C \Rightarrow \frac{-1}{5}\cos(5q) + C$