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Find the indefinite integral of `f(t) = 15*sin (3t) - 7e^(21t)`

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user1548464 | (Level 2) eNoter

Posted March 25, 2013 at 4:52 PM via web

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Find the indefinite integral of `f(t) = 15*sin (3t) - 7e^(21t)`

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted March 25, 2013 at 5:03 PM (Answer #1)

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The integral of `f(t) = 15*sin 3t - 7*e^(21*t)` has to be determined.

`int f(t) dt`

= `int 15*sin 3t - 7*e^(21*t) dt`

= `int 15*sin 3t dt - int 7*e^(21*t) dt`

`int 15*sin 3t dt`

let 3t = y, dy = 3*dt

= `int 5*sin y dy`

= `-5*cos y`

= `-5*cos(3t)`

`int 7*e^(21*t) dt`

let 21*t = y, dy = 21*dt

= `int (1/3)*e^y dy`

= `(1/3)*e^y`

= `e^(21*t)/3`

`int 15*sin 3t dt - int 7*e^(21*t) dt = -5*cos(3t) - e^(21*t)/3 + C`

The required integral is `-5*cos(3t) - e^(21*t)/3 + C`

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