Use the substitution x=3 cos t, 0 ≤ t ≤ π to simplify the following integral

Question

I'm doing the Mobius assignment here

Use the substitution  x=3 cos t, 0 ≤ t ≤ π  to simplify the following integral:

∫ 1 / sqrt(9 - x^2)

(a) Calculate sqrt(9 - x^2) in terms of t.

ans: 3*sin(t)

(b) If the substitution replaces dx with f(t) dt then what is the function f(t)?

ans: -3*sin(t)

(c) Hence write the integral in terms of t: ∫ dt

ans: -1

(d) Perform this integral, including constant of integration c.

ans: -t + C

(e) Convert your answer from a function of t to a function of x.

ans: -(cos^(-1))*(x/3)

for parts (a) to (d) I get the answer correct. but for part (e) the Mobius system said that my answer was wrong and one of my classmates commented "You need to include everything from the previous answer, you've left something out". But I am not sure what I left

Answer 1

You left out the constant of integration, C.

If it still complains, also, check whether the Mobius system wanted to put boundaries. It appears there is a suggestion that 0 ≤ t ≤ π.