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    Evaluation of Indefinite and Definite Integrals

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    (a) Find the indefinite integrals of the following functions
    (i) f(t)=27 cos(9t)+4e^(-12t)
    (ii) g(x)=(14+45x^3)/x (x >0)
    (iii) h(u)=(sin)^2 (1/4u)

    (b) Evaluate
    integration[3, 7]x(5x^2+9)dx
    (c) (i) Write down a definite integral that will give the value of the area under the curve
    y=x^3cos(2/5 x) between x=1/2pi and x = pi

    (The expression x^3cos(2/5 x) takes no negative values for 1/2pi ≤ x ≤ pi
    You are not asked to evaluate the integral by hand.)

    Provide a printout of your working for part (c)(ii).

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    (a)Find the indefinite integrals of the ...

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    The solution gives detailed steps on solving the indefinite and definite integrals. All formula and calculations are shown and explained.