(a) Use the Maclaurin series of cos(x) to state the rst three non-zero

terms of the Maclaurin series for (1-(cos(x))/(x^2)

x2 .

(b) Explain how you would use your answer in (a) to estimate

(integral from 0 to 1) (1-(cos(x))/(x^2) dx

This is a pretty complicated problem, but I got part a)

I got:

first derivative: -2(1-cos(x))(x^-3) + sinx(x^-2)

second derivative: 6(1-cos(x))(x^-4)-2(sinx)(x^-3)-2sinx(x^-3)+cosx(x^-2)

third derivative: -24(1-cosx)(x^-5)+6(sinx)(x^-4)+6sinx(x^-4)-2cosx(x^-3)+6sinx(x^-4)-2cosx(x^-3)-2cosx(x^-3)-sinx(x^-2)

From here, I know I am supposed to plug in (first derivative + second derivative + third derivative) in place of (1-(cos(x))/(x^2) to get the

(integral from 0 to 1) (1-(cos(x))/(x^2) dx, but I don't know how to integrate the whole thing. Please help! Thank you