CUET Mathematics - The value of the definite integral _0^1 e^x (1-x)^2/(1+x^2)^2dx is: | PYQs + Solutions

CUET Mathematics 2025 21 May Shift 2

Calculus

Hard

applied

$\frac{e}{2}$

$\frac{e}{2} - 1$

$\frac{e}{2} + 1$

$2e + 1$

✅ Correct Option: 2

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If $\int \frac{dx}{(x-1)^2(x+2)^2} = a[1 - g(x)]^b + c$ , where $c$ is a constant of integration, then which of the following are true?

(A) $a = \frac{1}{3}$

(B) $\beta = \frac{3}{4}$

(D) $g(x) = \frac{3}{(x+2)}$

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CUET Mathematics 2025 21 May Shift 2 PYQs