**Unformatted text preview: **5. Find the length of the curve deﬁned by [10] y = Z x 2 1 1 2 r 1-1 t dt , 2 ≤ x ≤ 3 . 6. Solve the following. [20] (a) Find the volume of the solid generated by revolving the region enclosed by y = x 2 + 1 and y = x + 3 about x = 3 . (b) Find the volume of the solid generated by revolving the region bounded by y = 1-( x-1) 2 and the x-axis about the x-axis. 7. Find the surface area of the spherical cap obtained by rotating around the x-axis the curve described [15] parametrically by y = a sin θ , x = a cos θ , ≤ θ ≤ π/ 6 (for any constant a > )....

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- Spring '07
- BERMAN
- Definite Integrals, Integrals, lower bounds, Practice Prelim