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Definite Integration question

2024 · Shift 2 · Q33

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PYQ Library
JEE Advanced
Mathematics
Definite Integration
2024 · Shift 2 · Q33

Definite Integration question

2024 · Shift 2 · Q33

JEE AdvancedMathematicsDefinite IntegrationNumerical+3 / −1

Let

f:\left[0, \frac{\pi}{2}\right] \rightarrow[0,1]

be the function defined by

f(x)=\sin ^2 x

and let

g:\left[0, \frac{\pi}{2}\right] \rightarrow[0, \infty)

be the function defined by

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

.The value of

2 \int\limits_0^{\frac{\pi}{2}} f(x) g(x) d x-\int\limits_0^{\frac{\pi}{2}} g(x) d x

is

\underline{\hspace{2cm}}

.

Numerical answer

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