If $$f(x)=$$∫$$x2+sin2$$⁡$$x1+x2sec2$$⁡xdx and $$f(0)=0$$, then $$f(1)=$$

Correct option is 4None of these

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$If f (x) = \int \frac{(x^{2} + \sin^{2} x)}{1 + x^{2}} \sec^{2} x d x and f (0) = 0, then f (1) =$

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1−π/4

π/4−1

tan⁡1−π/4

None of these

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detailed solution

Correct option is D

f(x)=∫x2+sin2⁡x1+x2sec2⁡xdx=∫x2+1−cos2⁡x1+x2sec2⁡xdx=∫sec2⁡x−11+x2dx=tan⁡x−tan−1⁡x+C∵f(0)=0, ∴C=0 Thus, f(x)=tan⁡x−tan−1⁡x Hence, f(1)=tan⁡1−tan−1⁡1=tan⁡1−π/4

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If f(x)=∫x2+sin2⁡x1+x2sec2⁡xdx and f(0)=0, then f(1)=

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

$If f (x) = \int \frac{(x^{2} + \sin^{2} x)}{1 + x^{2}} \sec^{2} x d x and f (0) = 0, then f (1) =$