Calculus and Above

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Indefinate integrals of (1) X^(-2/3)...

Indefinate integrals of (1) X^(-2/3) In(5x)dx (x>0) (11) Cosx/1+4sin^(2)x dx (a) (i) Explain why the graph of the function f(x) = (3x − pi) cos(1/2x) lies below the x-axis for −pi < x < 1/3pi and above the x-axis for 1/3pi< x < pi. (ii) Use this fact to find the area enclosed by the graph and the x-axis between x = −pi and x = pi, giving your answer to four decimal places. (b) Find the volume of the solid of revolution obtained when the graph of f(x) = tan x, from x = −1/6pi to x = 1/3pi, is rotated about the x-axis. Give your answer to four decimal places.

(a) Use the Taylor polynomials * p*1

(b) (i) Use multiplication of Taylor series to find the quartic Taylor

polynomial about 0 for the function

* f(x)=e^(-x)/1-x^(2)*evaluating the coefficients.

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