CUET · MATHS · PYQ PAPER 2023
\(\int_{0}^{\pi} e^x (\tan x + \sec^2 x) dx =\)
- A \(0\)
- B 1
- C -1
- D \(-e^x\)
Answer & Solution
Correct Answer
(A) \(0\)
Step-by-step Solution
Detailed explanation
\(\int e^x (f(x) + f'(x)) dx = e^x f(x)\) \(\int_{0}^{\pi} e^x (\tan x + \sec^2 x) dx = [e^x \tan x]_{0}^{\pi}\) \(= e^{\pi} \tan \pi - e^0 \tan 0\) \(= e^{\pi} \cdot 0 - 1 \cdot 0\) \(= 0\)
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