Posted by Tracy on .
Evaluate the integral sin4x cos^2 4x dx
A. cos^3 4x/3 +C
B. - cos^3 4x/3 +C
C. cos^3 4x/12 +C
D. -cos^3 4x/12 +C
Go on: wolframalpha dot com
When page be open in rectangle type:
integrate sin(4x) cos^2(4x) dx
and click option =
After few seconds when you see result click option: Show steps
On wolframalpha dot com you can practice any kind of calculus.
Notice that the derivative of the power cos^2 (4x) shows up as multiple, so we can just reverse the chain rule
I know that it must be something like (cos 4x)^3....
so from y ' = sin 4x (cos 4x)^2
we get y = sin 4x (cos 4x)^3 (1/3) (-1/sin 4x) (1/4)
= (-1/12) cos^3 (4x) )
which if you had used brackets correctly would have been C>