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:

Open MARKS Web Download App

Search any question & find its solution

Question: Answered & Verified by Expert

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:

MathematicsDefinite IntegrationJEE MainJEE Main 2015 (11 Apr Online)

Options:

A $\frac{\sqrt{3}}{2}$
B $\sqrt{3}$
C $\frac{1}{2}$
D $\sqrt{\frac{3}{2}}$

Solution:

1522 Upvotes Verified Answer

The correct answer is:

\sqrt{3}

\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}

.

Looking for more such questions to practice?

Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.

Use on iOS or Desktop Download from Google Play