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?

Question

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?

Quizplus · Accepted Answer

The Answer of 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?

Let g(x)=∫0xf(t)dtg ( x ) = \int _ { 0 } ^ { x } f ( t ) d tg(x)=∫0x​f(t)dt

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