Find Taylor series from first derivative of f(x)

The question asks for the seventh-degree Taylor series of a function whose first derivative is sin(x^2)

The question if from: Lagrange Error Bound with Answers (4/19) (Access Denied on Webb, Rhian / Calculus BC Worksheets & Answers

I have no clue on how to do this question.

Help me please! Thanks!

Re: Find Taylor series from first derivative of f(x)

How about finding the Taylor series for sin(x^2) and then integrate that series "term by term".

Re: Find Taylor series from first derivative of f(x)

Re: Find Taylor series from first derivative of f(x)

That is essentially the same thing as "since you know f', you can find f'', f''', etc." and plug those into the formula for Taylor's series. Of course, you cannot know the value of f itself at whatever point you centering this oh. That will be the "+ C" when you do the itegration using Kiwi Dave's method.