The value of ∫sin2x0sin−1(√t)dt+∫cos2x0cos−1(√t)dt is
π4
0
π2
None of these
Let f(x)=∫sin2x0sin−1(√t)dt+∫cos2x0cos−1(√t)dt Here f′(x)=0 ⇒ f(x)=c (a constant). But f(π4)=∫120(sin−1√t+cos−1√t)dt=∫120(π2)dt=π4