## anonymous one year ago 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=

1. anonymous

2. anonymous

@campbell_st

3. campbell_st

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

4. campbell_st

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

5. anonymous

So the area of the trapezoid would be 7.5

6. anonymous

and the area of the semicircle would be 1

7. anonymous

8. campbell_st

I don't have an answer list

9. anonymous

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

10. campbell_st

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