Antiderivatives plus piecewise function

JaysFanatic

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Jan 31, 2011
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5
Hi.

Express F(x) when x> 1. \(\displaystyle F(x) = \int_{0}^{x}f(t)dt\)

where \(\displaystyle f(t) = \left\{\begin{array}{cc}t^{2}, \;\ t\geq 1 \\ 2-t, \;\ t\leq 1\end{array}\)

I had no idea how to start the problem. I thought maybe we had to take the anitderivative of \(\displaystyle t^{2}\) to get \(\displaystyle \frac{t^{3}}{3} + c\), but I'm not sure. Any help would be welcome!
 
That is correct. Now do the other piece, substitute x and 0, and solve the rest of the problem.
 
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