Question

Evaluate the definite integral. use the integration capabilities of a graphing utility to verify your result. π/24 cos(12x) 0 dx

Answer 1

$\int\limits^\frac{\pi}{24}_0 {cos12x} \, dx$

I think this is what you are looking for.

The harder part is the find the intgral for cos(12x)

It has to be something like sin(12x) as we know that sin'=cos

Sin'(12x)= 12 cos(12x) which is not good as it is 12 times what we want.

So the integral of cos(12x) = 1/12 sin(12x) +C (constant)

Now to find the definite integral you need to plug in the values of the end points to the above integral and subtract.

1/12 sin0 = 0

1/12 sin(12*Pi/24)=1/12 * 1 = 1/12

Subtract bottom from top to get -1/12