4x²-9y², 8x³ - 27y³ and (2x-3y)²
1 answer:
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(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
So the area of
If you're not familiar with the error function
(b) Find the intersections of the line
So the area of
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