Let f ( x ) = e x 4 sin x and g ( x ) = e x cos x . Statement-I: ∫ 0 π /4 e x 4 sin x d x

Question

Let f ( x ) = e x 4 sin x and g ( x ) = e x cos x . Statement-I: ∫ 0 π /4 ​ e x 4 sin x d x < ∫ 0 π /4 ​ e x cos x d x Statement-II: If f ( x ) < g ( x ) for all x ∈ [ a , b ] , then ∫ a b ​ f ( x ) d x ≤ ∫ a b ​ g ( x ) d x

TestHub · Accepted Answer

e x 2 cos x < e x sin x for ∀ x ∈ [ 0 , 4 π ​ ) integrate both the sides ∫ 0 π /4 ​ e x 2 cos xdx < ∫ 0 π /4 ​ e x sin xdx Statement-II is also correct.

Mathematics - Definite Integration Question with Solution | TestHub

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