math
posted by arun .
1) A region is bounded by the line y = x and the parabola y = x2  6x + 10. What is the volume of the solid generated by revolving the region about the xaxis?

First define the x limits of the enclosed region. They are between the two roots of
x^2 6x +10 = x
x^2 7x +10 = 0
(x  5)(x 2)= 0
You want to integrate between x = 2 and 5.
The function that you integrate is
f(x) = pi*{[x^2 6x +10]^2 + x^2} dx.
The y = x curve lies above the parabola in the interval