Evaluate the integral of (sin x + cos x)² dx
Solution. Simplify the integral function:
(sinx+cosx)2=sin2x+cos2x+2sinxcosx=1+sin(2x).( sinx+cosx)^2=sin^2x+cos^2x+2sinxcosx=1+sin(2x).(sinx+cosx)2=sin2x+cos2x+2sinxcosx=1+sin(2x).
Then: ∫(sinx+cosx)2dx=∫(1+sin(2x))dx=x−12cos(2x)+constant.\intop(sinx+cosx)^2dx=\intop(1+sin(2x))dx=x-\frac{1}{2}cos(2x)+\rm constant.∫(sinx+cosx)2dx=∫(1+sin(2x))dx=x−21cos(2x)+constant.
Answer: ∫(sinx+cosx)2dx=x−12cos(2x)+constant.\intop(sinx+cosx)^2dx=x-\frac{1}{2}cos(2x)+\rm constant.∫(sinx+cosx)2dx=x−21cos(2x)+constant.
Need a fast expert's response?
and get a quick answer at the best price
for any assignment or question with DETAILED EXPLANATIONS!
Comments
Leave a comment