If the value of the definite integral A = ∫ 0 10 π sin ⁡ x d x is equal to k π , then the absolute value of k is equal to (where, ⋅ is the greatest integer function)

Question

If the value of the definite integral A = ∫ 0 10 π sin ⁡ x d x is equal to k π , then the absolute value of k is equal to (where, ⋅ is the greatest integer function),

MARKS App · Accepted Answer

As period of sin ⁡ x is 2 π , I = 5 ∫ 0 2 π sin ⁡ x d x I = 5 ∫ 0 π 0 d x + ∫ π 2 π - 1 d x = 5 - x π 2 π = - 5 π ∴ k = - 5 ⇒ k = 5

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