JEE Mains · Maths · STD 12 - 7.2 definite integral
Let \(f : (-1, 1) \to R\) be a continuous function. If \(\int\limits_0^{\sin \,x} {f\left( t \right)dt} = \frac{{\sqrt 3 }}{2}x\) , then \(f\left( {\frac{{\sqrt 3 }}{2}} \right)\) is equal to
- A \(\frac{1}{2}\)
- B \(\frac{{\sqrt 3 }}{2}\)
- C \(\sqrt {\frac{3}{2}} \)
- D \(\sqrt 3 \)
Answer & Solution
Correct Answer
(D) \(\sqrt 3 \)
Step-by-step Solution
Detailed explanation
Let \(f:\left( { - 1,1} \right) \to R\) be a continuous function Let \(\int\limits_0^{\sin x} {f\left( t \right)dt} = \frac{{\sqrt 3 }}{2}x\) \(f\left( {\sin x} \right).\frac{d}{{dx}}\left( {\sin x} \right) = \frac{{\sqrt 3 }}{2}\)…
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