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JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Analyzing +4 | -1
Given (x)=∣ 0x2−sin⁡  xcos⁡  x−2sin⁡  x−x201−2x2−cos⁡  x2x−10∣,   ∫f(x)dx\left( x \right) = \left| {\,\begin{array}{cccccccccccccccccccc} 0&{{x^2} - \sin \,\,x}&{\cos \,\,x - 2}\\ {\sin \,\,x - {x^2}}&0&{1 - 2x}\\ {2 - \cos \,\,x}&{2x - 1}&0 \end{array}} \right|,\;\,\int f\left( x \right)dx is equal to
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Correct option: D
None of these
The correct answer is 43\frac{4}{3} because the integral of the odd part is zero, and the integral of the even part is calculated correctly.

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