Mathematics

Problem

The curve

y=2x^{3/2}-5x^{-1/3}+4

is considered on the interval

1\le x\le4

. a. (i) Find the antiderivative

H(x)

y

and write it in simplest form. b. (ii) Using your result from part (i), evaluate

\displaystyle \int_{1}^{4}\bigl(2x^{3/2}-5x^{-1/3}+4\bigr)\,dx

. c. (iii) State what the numerical value obtained in part (ii) represents with respect to the given curve and the

x

–axis on

[1,4]

. (No sketch is required.)