If $$f(x)=$$$$cos$$⁡x−$$cos2$$⁡$$x+cos3$$⁡x−…∞ then ∫$$f(x)d$$¨x is equal to

Correct option is 2x-tan⁡x2+C

Questions

If $f (x) = \cos x - \cos^{2} x + \cos^{3} x - \dots \infty$ then $\int f (x) \ddot{d} x$ is equal to

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tan⁡x2+C

x-tan⁡x2+C

x−12tan⁡x2+C

x−tan⁡x22+C

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detailed solution

Correct option is B

∵f(x)=cos⁡x−cos2⁡x+cos3⁡x−…∞=cos⁡x1+cos⁡x∴∫f(x)dx=∫1+cos⁡x1+cos⁡xdx−∫11+cos⁡xdx =x−12∫sec2⁡x2dx =x−12tan⁡x2⋅2+C=x−tan⁡x2+C

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If f(x)=cos⁡x−cos2⁡x+cos3⁡x−…∞ then ∫f(x)d¨x is equal to

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

If $f (x) = \cos x - \cos^{2} x + \cos^{3} x - \dots \infty$ then $\int f (x) \ddot{d} x$ is equal to