CUET · MATHS · PYQ PAPER 2023
The value of \(\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}\left(x^5+x^3+x+2\right) d x\) is:
- A \(0\)
- B 2
- C \(2 \pi\)
- D \(\pi\)
Answer & Solution
Correct Answer
(C) \(2 \pi\)
Step-by-step Solution
Detailed explanation
\(\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}\left(x^5+x^3+x+2\right) d x = 2\int_{0}^{\frac{\pi}{2}} 2 d x\) \(= 2[2x]_{0}^{\frac{\pi}{2}} = 2\left(2 \cdot \frac{\pi}{2} - 0\right) = 2\pi\)
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