If ∫ 0 π x f ( sin x ) d x = A ∫ 0 π /2 f ( sin x ) d x , then A is

Let I = ∫ 0 π x f ( sin x ) d x = ∫ 0 π ( π − x ) f ( sin x ) d x = π ∫ 0 π f ( sin x ) d x − I ( sin ce f ( 2 a − x ) = f ( x )) ⇒ I = π ∫ 0 π /2 f ( sin x ) d x ⇒ A = π

Home

Mathematics - Definite Integration Question with Solution | TestHub

MathematicsDefinite IntegrationDefinite Integration by SubstitutionMedium2 minPYQ_2004

MathematicsMediumsingle choice

If $\int_{0}^{π} x f (sin x) d x = A \int_{0}^{π /2} f (sin x) d x$ , then $A$ is

Options:

Answer:

Solution:

Let $I = \int_{0}^{π} x f (sin x) d x = \int_{0}^{π} (π - x) f (sin x) d x = π \int_{0}^{π} f (sin x) d x - I (sin ce f (2 a - x) = f (x))$ $\Rightarrow I = π \int_{0}^{π /2} f (sin x) d x \Rightarrow A = π$

Stream:JEESubject:MathematicsTopic:Definite IntegrationSubtopic:Definite Integration by Substitution

⏱ 2mℹ️ Source: PYQ_2004

Doubts & Discussion

Loading discussions...