Can someone help me please I donโt know why Iโm ending up with wrong answer even I use calculator โฆ Iโm not confident although every time I got same answer but the textbook answer is wrong โฆ The method is correct but answer only wrong โฆ So please help me friends

Whatโs the question? You should at least post the question so that people can know what is going on?

## Question

In the diagram on the right, the curve y^{2}=4-x and the straight line y=x-2 intersect at two points, A and B.

Find

(a) the coordinates of A,

(b) the coordinates of B,

(c) the generated volume, in terms of \pi, when the enclosed shaded region by the curve y^{2}=4-x and the straight line y=x-2 is rotated through 360^{\circ} about the y-axis.

### Answer

Hi Dhaksheina, I think you made a sign error:

It should be:

y^2=4-x and x=4-y^2

Here is my working for your reference:

Note that I used the volume of a cone formula instead of integrating the straight line as it is faster, but your method works fine too!

Do let me know if my answer differs from the textbook and feel free to clarify if you have any doubts!