Find the Integral value of f(x) = x * sinx within the limits 0, π.

(A) π
(B) 2π

(C) π/2

(D) 0

Answer: (A)

Explanation:
Let I = ∫x*sinx ———————————————————-> 1

I = ∫( π-x)*sin(π-x) = ∫(( π-x)*sin(x) —————- 2

Adding both 1 and 2

=> I + I = ∫ π*sinx = π*[-cosx] = – π*[cos π – cos0]

=> 2I = – π*-2

=> I = π

The value of Integral is π


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