∫cos3x dx = ______. - Mathematics and Statistics

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MCQ
Fill in the Blanks

`int cos^3x  dx` = ______.

Options

  • `1/12 sin 3x + 3/4 sin  x + c`

  • `1/12 sin 3x + 1/4 sin x + c`

  • `1/12 sin 3x - 3/4 sin x + c`

  • `1/12 sin 3x - 1/4 sin x + c`

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Solution

`int cos^3x  dx` = `underlinebb(1/12 sin  3x + 3/4 sin  x + c)`.

Explanation:

`int cos^3x . dx`

cos 3A = 4 cos3 A – 3 cos A

I = `int 1/4 (cos 3x + 3 cos x) . dx`

= `1/4 (sin 3x . 1/3 + 3 . sin x) + c`

= `1/12 sin 3x + 3/4 sin x + c`

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2022-2023 (March) Official

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