Given,$$f(x)=0x2$$−$$sin$$ ⁡xcos ⁡x−$$2sin$$ ⁡x−$$x201$$−$$2x2$$−$$cos$$⁡ $$x2x$$−$$10$$' then ∫$$f(x)dx$$ is equal to

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Given,$$f(x)=0x2$$−$$sin$$ ⁡xcos ⁡x−$$2sin$$ ⁡x−$$x201$$−$$2x2$$−$$cos$$⁡ $$x2x$$−$$10$$' then ∫$$f(x)dx$$ is equal to

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We have,            ⇒        $$f(x)=0x2$$−$$sin$$ ⁡xcos ⁡x−$$2sin$$ ⁡x−$$x201$$−$$2x2$$−$$cos$$ ⁡$$x2x$$−$$10f(x)=0sin$$⁡ x−$$x22$$−$$cos$$ ⁡ $$xx2$$−$$sin$$ ⁡$$x02x$$−$$1cos$$ ⁡x−$$21$$−$$2x0$$[interchanging rows and columns]⇒$$f(x)=($$−$$1)30x2$$−$$sin$$ ⁡xcos⁡ x−$$2sin$$⁡ x−$$x201$$−$$2x2$$−$$cos$$ ⁡$$x2x$$−$$10$$[taking $$(-1)$$ common from each column]⇒ $$f(x)=$$−$$f(x)$$⇒$$f(x)=0$$⇒ ∫$$f(x)dx=c$$

Given, $f (x) = |\begin{array}{ccc} 0 & x^{2} - \sin x & \cos x - 2 \\ \sin x - x^{2} & 0 & 1 - 2 x \\ 2 - \cos x & 2 x - 1 & 0 \end{array}|$ ' then $\int f (x) dx$ is equal to

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Given,f(x)=0x2−sin ⁡xcos ⁡x−2sin ⁡x−x201−2x2−cos⁡ x2x−10' then ∫f(x)dx is equal to

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Given, $f (x) = |\begin{array}{ccc} 0 & x^{2} - \sin x & \cos x - 2 \\ \sin x - x^{2} & 0 & 1 - 2 x \\ 2 - \cos x & 2 x - 1 & 0 \end{array}|$ ' then $\int f (x) dx$ is equal to