GATE | GATE MOCK 2017 | Question 11
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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