Paragraph Let f : [0, (π)/2 ] → [0,1] be the function defined by f(x) = sin^2 x and let g : [0, (π)/2 ] → [0, ∞) be the function defined by g(x) = √((π x)/2 - x^2). The value of 16/(π^3) displaystyleint_0^(π)/2 f(x)g(x)dx is ___________.

Paragraph Let f : [0, (π)/2 ] → [0,1] be the function… — JEE Advanced 2024 Mathematics PYQ

JEE Advanced 2024 · Paper 2 · numerical answer

Paragraph
Let

f : \left[0, \dfrac{\pi}{2}\right] \to [0,1]

be the function defined by

f(x) = \sin^2 x

and let

g : \left[0, \dfrac{\pi}{2}\right] \to [0, \infty)

be the function defined by

g(x) = \sqrt{\dfrac{\pi x}{2} - x^2}

.

The value of

\dfrac{16}{\pi^3} \displaystyle\int_{0}^{\frac{\pi}{2}} f(x)g(x)dx

is ___________.

Show answer

Answer: 0.25

[JEE Advanced 2024 · Paper 2]

Practise Definite Integrals and Areas the way it is asked

A timed set of real JEE Advanced Definite Integrals and Areas questions, graded as the exam grades. No sign-up.