Crazy Function!

Calculus Level 4

Function f(x) is given by \textbf{Function f(x) is given by} f ( x ) = ∫ 0 s i n 2 x sin ⁡ − 1 t d t + ∫ 0 c o s 2 x cos ⁡ − 1 t d t f(x) = \int_{0}^{sin^{2}x} \sin^{-1}\sqrt{t} dt + \int_{0}^{cos^{2}x} \cos^{-1}\sqrt{t} dt

Find \textbf{Find} f ( π 2 ) f(\sqrt{\frac{π}{2}})

x belongs in the interval [0,π/2] \textbf{x belongs in the interval [0,π/2]}


The answer is 0.785.

Avineil Jain by Avineil Jain , 24, Netherlands

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1 solution

Vishal Sharma
Apr 11, 2014

Differentiate the function to realize that it is a constant function. Therefore, we can find f ( p i 4 ) f(\frac{pi}{4})

The easiest to compute...

2 Helpful 0 Interesting 0 Brilliant 0 Confused

but how to find the constant value??

Souradeep Roy Choudhury - 6 years, 8 months ago

plz explain

Rahul Jain - 5 years, 11 months ago

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