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For x in (0, pi/2), evaluate: I = integral from 0 to sin²(x) of arcsin(sqrt(t)) dt + integral from 0 to cos²(x) of arccos(sqrt(t)) dt.

1. pi/2
2. 1
3. pi/4
4. None of these

Correct answer: pi/4

Solution

After substituting t = sin²(u) and t = cos²(u) in the two integrals respectively, they merge into the definite integral from 0 to pi/2 of u*sin(2u) du = pi/4.

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