TS EAMCET · Maths · Definite Integration
It is given that \[ \frac{d}{d t}(t \log t-t)=\log t \text { then } \exp \left(\int_0^1 2 x \log \left(1+x^2\right) d x\right)= \]
- A \(\mathrm{e}\)
- B 2
- C \(\frac{4}{e}\)
- D \(\frac{e}{4}\)
Answer & Solution
Correct Answer
(C) \(\frac{4}{e}\)
Step-by-step Solution
Detailed explanation
Given \(\frac{d}{d t}(t \log t-t)=\log t\) Take, \(\exp \left(\int_0^1 2 x \log \left(1+x^2\right) d x\right)\) Let \(1+x^2=t\) \(2 x d x=d t\) when \(x=0, t=1\) \(x=1, t=2\) Then, \(\exp \left(\int_1^2 \log t-d t\right)=\left.\exp (t \log t-t)\right|_1 ^2\)…
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