Evaluate the integrals \sqrt{\frac{1-\cos x}{2}}dx

ediculeN

ediculeN

Answered question

2021-10-06

Evaluate the integrals
1cosx2dx

Answer & Explanation

Raheem Donnelly

Raheem Donnelly

Skilled2021-10-07Added 75 answers

Consider the given integral 02π1cosx2dx
Use the property of cosx=12sin2x2
02π1cosx2dx=02π1(12sin2x2}{2}dx
=02π2sin2x22dx
=02π2sin2x22dx
=02π2sin2x22dx
=02πsin2x2dx
As we know that a2=|a|
02π1cosx2dx=02π|sinx2|dx
But |sinx2|=sinx2 because interval given (0,2π)
02π1cosx2dx=02πsinx2dx
=[(cosx2)12]02π
=2(cos2π2=cos0)
=2(cosπcos0)

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