(a) Find the volume of the solid generated by revolving area about th…

Previous year question for Engineering Mathematics-I.

Question

(a) Find the volume of the solid generated by revolving area about the x-axis, of the area included between $y^2 = x^3$ and $x^2 = y^3$.

(b) Evaluate $\int_{0}^{\infty} x^3 \cdot e^{-\sqrt{x}} dx$.

(c) Evaluate $\int_{-1}^{1} (1 + x)^{3/2} (1 - x)^{7/2} dx$ by using beta/gamma functions.

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