Inverse sine function integral: definite integral pi(arcsin(y))^2 trig sub integral, let y=sin(x).

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Integral arcsine squared:

When we integrate an inverse trig function, we make a trigonometric substitution that undoes the inverse function. In this case, we have an inverse sine function integral, so we to integrate inverse sine, we let y=sin(x) or y=sin(theta) etc.

After transforming the inverse sine function integral in terms of a new variable, we transform the limits of integration as well, and we are left with a classic integration by parts integral.