CUET · MATHS · PYQ PAPER 2025
The value of the definite integral \(\int_0^1 e^x \frac{(1-x)^2}{\left(1+x^2\right)^2} d x\) is :
- A \(\frac{e}{2}\)
- B \(\frac{e}{2}-1\)
- C \(\frac{e}{2}+1\)
- D \(2 e+1\)
Answer & Solution
Correct Answer
(B) \(\frac{e}{2}-1\)
Step-by-step Solution
Detailed explanation
\(\int_0^1 e^x \frac{(1-x)^2}{\left(1+x^2\right)^2} d x = \int_0^1 e^x \frac{1+x^2-2x}{\left(1+x^2\right)^2} d x\) \(= \int_0^1 e^x \left( \frac{1}{1+x^2} - \frac{2x}{\left(1+x^2\right)^2} \right) d x\) Using \(\int e^x (f(x) + f'(x)) d x = e^x f(x)\), with…
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