Question Detail
Question
A certain substitution gives ∫sin²x·cosⁿx dx = ∫uⁿ - u⁷ du. What is n?
Correct Answer
Option C is the correct answer.
Detailed Explanation
With u=sinx (or cosx depending on setup) so that sin²x·cosⁿx becomes a polynomial in u, matching the u⁷ term in the result requires the original cosine power to be n=7, consistent with a standard odd-power trig substitution.
Hint
Think about which substitution turns sin²x cosⁿx dx into a difference of two pure powers of u.