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Definite Integration question

2024 · 31 Jan · Shift 1 · Q60

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JEE Main
Mathematics
Definite Integration
2024 · 31 Jan · Shift 1 · Q60

Definite Integration question

2024 · 31 Jan · Shift 1 · Q60

JEE MainMathematicsDefinite IntegrationNumerical+4 / −1

Let

f: \mathbb{R} \rightarrow \mathbb{R}

be a function defined by

f(x)=\frac{4^x}{4^x+2}

and

M=\int_{f(a)}^{f(1-a)} x \sin ^4(x(1-x)) d x, N=\int_{f(a)}^{f(1-a)} \sin ^4(x(1-x)) d x ; a eq \frac{1}{2}

. If

\alpha M=\beta N, \alpha, \beta \in \mathbb{N}

, then the least value of

\alpha^2+\beta^2

is equal to

\underline{\hspace{2cm}}

.

Numerical answer

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