Integral of Sin 2x

When evaluating definite integrals by substitution one may calculate the antiderivative fully first then apply the boundary conditions. We solve this equation for the desired integral and find that secn-2x tan x n 2 sec 2 x d.

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Find the area of the surface generated by revolving the curve y cosh x 0 x 1 around the x-axis.

. There were no integral boundaries to transform but in the last step reverting the original substitution was necessary. For example if we take n. See x dx This is the desired reduction formula.

2 2 cos O sin 0 1 sin x sec x Sin X dx sin 2x 99. In that case there is no need to transform the boundary terms.

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