Diagram shows a curve and a straight line which is tangent to the curve at the point
a)calculate the area of the shaded region.
Oh, I didn't notice you were rotating around the y-axis my bad...
Right, we use the formula:
Since you are rotating through the y-axis, you need the y coordinates.
So, we get:
y = 7 - 4x
x = (7 - y)/4
y = 4 - x^2
x = \sqrt(4 - y)