- #1
BioCore
Homework Statement
Hi, I have a test coming up soon so I was doing some questions from the textbook when I stumbled upon this one and I'm stuck after like 5 tries. Here is the question:
[tex]\int[/tex]cos^2(x)dx
Solve.
Homework Equations
the question then states we should solve using this:
cos^2(x)dx = (cos x)(cos x)
which gives us:
[tex]\int[/tex]cos^2(x)dx = sinxcosx + [tex]\int[/tex]sin^2(x)dx
finally we should use sin^2(x) + cos^2(x) = 1 to replace the sin^2(x) at the right side of integral.
The Attempt at a Solution
so basically I tried using integral by parts, since we are studying this topic currently
and set:
u= 1 - cos^2(x) and dv = dx
du = 2cosxsinx and v = x
When I plug in the values into the integration and try to solve I don't end up with their answer. I must be overlooking something and this is where I am stuck:
[tex]\int[/tex]cos^2(x)dx = sinxcosx + x(1-cos^2x) - [tex]\int[/tex]2xcosxsinx
The final answer should be:
[tex]\int[/tex]cos^2(x)dx = 1/2sinxcosx + 1/2x + C
Thanks for the help.