calculus problem help!?

antideriv(sin(x)^2)dx evaluate using integration by parts

give answer in form (-1/A) (sin(Bx) cos(Dx)) + (1/F)x + c. i need A, B, D, and F.

please explain in detail how to do this. i do not just want an answer.

Top 2 Answers

A few days ago

Anonymous

Favorite Answer

Integrating by parts:

int sin^2(x) dx

= -int sin(x) d(cos(x))

= – [ sin(x)cos(x) – int cos(x) d(sin(x) ]

= – sin(x)cos(x) + int cos^2(x)

= – sin(x)cos(x) + int [ 1 – sin^2(x) ] dx

= – sin(x)cos(x) + x – int sin^2(x) dx

Addint int sin^2(x) to each side:

2 int sin^2(x) dx = -sin(x)cos(x) + x + const

int sin^2(x) dx = -(1/2)sin(x)cos(x) + (1/2)x + c

Hence:

A = 2, B = 1, D = 1, F = 2.

A few days ago

Anonymous

for such problems you should have a special math book were you can find addition theorems

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