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# Let $\displaystyle g(x) = \int^x_0 f(t) \,dt$, where $f$ is the function whose graph is shown.(a) Evaluate $g(0)$ and $g(6)$(b) Estimate $g(x)$ for $x$ = 1, 2, 3, 4, and 5.(c) On what interval is $g$ increasing?(d) Where does $g$ have a maximum value?(e) Sketch a rough graph of $g$.(f) Use the graph in part (e) to sketch the graph of $g'(x)$. Compare with the graph of $f$.

## a. Estimate integralb. Estimate integralc. $9^{\prime} \geq 0 \Rightarrow f \geqslant 0 \quad[0,3]$d. $g^{\prime}=0 \Rightarrow f=0 \quad x=3$e. graphf. graph

Integrals

Integration

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Ohio State University

Integrals

Integration

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