The graph of y = g(x) is shown below, where the curve below the axis is a semi-circle. The value of integral (0,8) g(x) dx=

Question

nathanjhw · Answer

attachment

nathanjhw · Answer

@campbell_st

campbell_st · Answer

well a simple method is to find the area of the trapizoid... parallel sides 4 and 1 and height of  3

then add the area of a semi-circle... radius 2

that's one way

campbell_st · Answer

that's the area under the curve... 

if you are just after a numerical value 

the semicircle has a negative area and the trapezoid has a positive area... 

so this will give a lesser value

nathanjhw · Answer

So the area of the trapezoid would be 7.5

nathanjhw · Answer

and the area of the semicircle would be 1

nathanjhw · Answer

so the answer is d

campbell_st · Answer

I don't have an answer list

nathanjhw · Answer

Oh the answer is pi(e^2/2 -1)

campbell_st · Answer

well the area of the semi circle is 

$$A = 2\pi$$

the area of the trapezium is 7.5 by you caclulation. 

because the area of the semi-circle is below the x axis the value is negative

so I'd say the value 

$$\int\limits_{0}^{8}g(x)~ dx = 7.5 - 2\pi$$

if you want the area then semi circle has a positive value... 

I have no idea what the question is asking for... I just gace you a quick solution to what is in the graph