`f'''(t) = cos(t)` Find `f`.

Textbook Question

Chapter 4, 4.9 - Problem 29 - Calculus: Early Transcendentals (7th Edition, James Stewart).
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gsarora17 | (Level 2) Associate Educator

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`f'''(t)=cos(t)`

`f''(t)=intf'''(t)dt`

`f''(t)=intcos(t)dt`

`f''(t)=sin(t)+c_1`

`f'(t)=int(sin(t)+c_1)dt`

`f'(t)=-cos(t)+c_1t+c_2`

`f(t)=intf'(t)dt`

`f(t)=int(-cos(t)+c_1t+c_2)dt`

` f(t)=-sin(t)+(c_1t^2)/2+c_2t+c_3`

c_1,c_2 and c_3 are constants.

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