Let f : ( - 1 , 1 ) → R be a continuous function. If ∫ 0 sin ⁡ x f ( t ) d t = 3 2 x , then f 3 2 is equal to:

∫ 0 s i n x f t d t = 3 2 x . Differentiating w.r.t x both the sides, f sin ⁡ x · cos ⁡ x = 3 2 Put x = π 3 . 1 2 · f 3 2 = 3 2 f 3 2 = 3 .

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Mathematics - Definite Integration Question with Solution | TestHub

MathematicsDefinite IntegrationMiscellaneous/MixedHard2 minPYQ_2015

MathematicsHardsingle choice

Let $f : (- 1, 1) \to R$ be a continuous function. If $\int_{0}^{\sin x} f (t) d t = \frac{\sqrt{3}}{2} x,$ then $f (\frac{\sqrt{3}}{2})$ is equal to:

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Answer:

Solution:

$\int_{0}^{s i n x} f (t) d t = \frac{\sqrt{3}}{2} x .$

Differentiating w.r.t $x$ both the sides,

$f (\sin x) \cdot \cos x = \frac{\sqrt{3}}{2}$

Put $x = \frac{π}{3}$ .

$\frac{1}{2} \cdot f (\frac{\sqrt{3}}{2}) = \frac{\sqrt{3}}{2}$

$f (\frac{\sqrt{3}}{2}) = \sqrt{3}$ .

Stream:JEESubject:MathematicsTopic:Definite IntegrationSubtopic:Miscellaneous/Mixed

⏱ 2mℹ️ Source: PYQ_2015

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