Calculus and Above

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lies below the x-axis for...

a) i) Explain why the graph of the function f(x)=(x^2+1)ln(x/2) lies below the x-axis for 1<x<2 and above the x-axis for 2<x<3.

ii) Use this fact to find the area enclosed by the graph and the x-axis between x=1 and x=3, giving you answer to five decimal places.

b) Find the volume of the solid of revolution obtained when the graph of f(x)=secx+tanx, from x= -Pi/3 to x = Pi/4 is rotated about the x-axis. Give you answer to four decimal places.

ii) Use this fact to find the area enclosed by the graph and the x-axis between x=1 and x=3, giving you answer to five decimal places.

b) Find the volume of the solid of revolution obtained when the graph of f(x)=secx+tanx, from x= -Pi/3 to x = Pi/4 is rotated about the x-axis. Give you answer to four decimal places.

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