English

Dx∫dxsin2xcos2x is equal to ______.

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Question

`int "dx"/(sin^2x cos^2x)` is equal to ______.

Options

  • tanx + cotx + C

  • x + cotx)2 + C

  • tanx – cotx + C

  • (tanx – cotx)2 + C

MCQ
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Solution

`int "dx"/(sin^2x cos^2x)` is equal to tanx – cotx + C.

Explanation:

I = `int ("d"x)/(sin^2x cos^2x)`

= `int ((sin^2x + cos^2x)"d"x)/(sin^2xcos^2x)`

= `int sec^2 x"d"x + int "cosec"^2x "d"x`

= tanx – cotx + C

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Chapter 7: Integrals - Solved Examples [Page 159]

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NCERT Exemplar Mathematics Exemplar [English] Class 12
Chapter 7 Integrals
Solved Examples | Q 21 | Page 159

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