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Find the integral integrate of sin(5x)cos(2x) dx

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master451 | Student | Honors

Posted October 8, 2012 at 2:31 PM via web

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Find the integral

integrate of sin(5x)cos(2x) dx

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sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted October 8, 2012 at 4:53 PM (Answer #1)

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You should convert the product in sum such that:

`sin(5x) cos(2x) = (1/2)(sin (5x - 2x) + sin(5x + 2x))`

Hence, evaluating the integral yields:

`int sin(5x) cos(2x) dx= (1/2)int (sin (3x) + sin(7x)) dx`

Using the linearity yields:

`int sin(5x) cos(2x) dx = (1/2)int (sin (3x)) dx + (1/2) int (sin(7x)) dx`

`int sin(5x) cos(2x) dx = (1/2)(-(cos(3x))/3 - (cos(7x))/7) + c`

Hence, evluating the given integral yields `int sin(5x) cos(2x) dx = (1/2)(-(cos(3x))/3 - (cos(7x))/7) + c.`

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