Let $g ( x ) = \int _ { 0 } ^ { x } f ( t ) d t$

question 219

Essay

Let $g ( x ) = \int _ { 0 } ^ { x } f ( t ) d t$ where f is the function whose graph is shown below: (a) Use the Comparison Properties of Integrals to estimate the value of the following integrals:
(i) $\int _ { 0 } ^ { 3 } f ( t ) d t$ (ii) $\int _ { 3 } ^ { 6 } f ( t ) d t$ (iii) $\int _ { 6 } ^ { 9 } f ( t ) d t$ (iv) $\int _ { 9 } ^ { 10 } f ( t ) d t$ (b) At what values of x does g have a local maximum or minimum?
(c) At what values of x does g attain its absolute maximum or minimum?

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