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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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