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  • Integral of the power products following integral: int_0^(pi 2)sen^2 . . .
    Explanation: Recall the identity #sin^2theta=1 2 (1-cos2theta)# Then, #sin^2 (theta 3)=1 2 (1-cos ( (2theta) 3)# Thus, we have #1 2int_0^ (pi 2) (1-cos ( (2theta) 3
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    -1 (3sin^3x) + c This intergal can be computed using an appropriate u substitution Letting u = sintheta then du = costheta d theta Hence int costheta (sin^4theta) d theta becomes int (du) u^4 = int u^-4 du therefore -1 3 u^-3 + c Hence via considering u = sintheta The antiderivative is -1 (3sin^3theta) + c
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