Step-by-step explanation:
x = 1, y = 5
x = 2, y = 3
x =3, y= 1
x=4 y=-1
12:7
12(2):7(2)
24:14
12:7 = 24:14
I hoped I helped(:
2
to work it out just go output f (x) - input x so, 3 - 1 = 2 and double check this using your next equations 4 - 2 = 2
(a) First find the intersections of

and

:

So the area of

is given by

If you're not familiar with the error function

, then you will not be able to find an exact answer. Fortunately, I see this is a question on a calculator based exam, so you can use whatever built-in function you have on your calculator to evaluate the integral. You should get something around 0.5141.
(b) Find the intersections of the line

with

.

So the area of

is given by


which is approximately 1.546.
(c) The easiest method for finding the volume of the solid of revolution is via the disk method. Each cross-section of the solid is a circle with radius perpendicular to the x-axis, determined by the vertical distance from the curve

and the line

, or

. The area of any such circle is

times the square of its radius. Since the curve intersects the axis of revolution at

and

, the volume would be given by