CUET · MATHS · PYQ PAPER 2023
The value of the integral \(\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}\left(x+x^3+x^5\right) d x\) is:
- A 2
- B 1
- C 0
- D \(\pi / 2\)
Answer & Solution
Correct Answer
(C) 0
Step-by-step Solution
Detailed explanation
\(f(x) = x+x^3+x^5\) \(f(-x) = (-x)+(-x)^3+(-x)^5 = -x-x^3-x^5 = -(x+x^3+x^5) = -f(x)\) Since \(f(x)\) is an odd function and the interval is symmetric \(\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]\), \(\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}\left(x+x^3+x^5\right) d x = 0\)
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