JEE Mains · Maths · STD 12 - 7.2 definite integral
If \(\int \limits_0^1 \frac{1}{\left(5+2 x -2 x ^2\right)\left(1+ e ^{(2-4 x)}\right)} dx =\frac{1}{\alpha} \log _{ e }\left(\frac{\alpha+1}{\beta}\right)\) \(\alpha, \beta > 0\), then \(\alpha^4-\beta^4\) is equal to:
- A \(21\)
- B \(0\)
- C \(19\)
- D \(-21\)
Answer & Solution
Correct Answer
(A) \(21\)
Step-by-step Solution
Detailed explanation
\(I=\int \limits_0^1 \frac{d x}{\left(5+2 x-2 x^2\right)\left(1+ e ^{2-4 \pi}\right)}\) \(x \rightarrow 1-x\) \(I=\int \limits_0^1 \frac{e^{2-4 x} d x}{\left(5+2 x-2 x^2\right)\left(1+ e ^{2-4 x}\right)}\) Add \((i)\) and \((ii)\)…
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