Answer to Question #167813 in Calculus for Phyroe

Question #167813

Evaluate the integral of (sin x + cos x)² dx


1
Expert's answer
2021-03-15T04:58:47-0400

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).

Then: (sinx+cosx)2dx=(1+sin(2x))dx=x12cos(2x)+constant.\intop(sinx+cosx)^2dx=\intop(1+sin(2x))dx=x-\frac{1}{2}cos(2x)+\rm constant.

Answer: (sinx+cosx)2dx=x12cos(2x)+constant.\intop(sinx+cosx)^2dx=x-\frac{1}{2}cos(2x)+\rm constant.


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