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The value $I = \int_{- 1}^{1} (\cos^{- 1} x + \frac{x^{7} - 3 x^{5} + 7 x^{3} - x}{\cos^{2} x}) d x$ is

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Correct option is D

Let f(x)=x7−3x5+7x3−xcos2x then f(−x)=−f(x) so ∫−11 f(x)dx=0 (Property 12)Let g(x)=cos−1⁡ x then I1=∫−11 cos−1⁡ xdx=∫−11 cos−1⁡ (−x)dx (Property 8)=∫−11 π−cos−1⁡ xdx=2π−I1Thus I=I1=π.

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The value I=∫−11 cos−1⁡x+x7−3x5+7x3−xcos2⁡xdx is

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The value $I = \int_{- 1}^{1} (\cos^{- 1} x + \frac{x^{7} - 3 x^{5} + 7 x^{3} - x}{\cos^{2} x}) d x$ is