Question

using the same substitution u = sin(x) enables us to do ∫19 sin4⁴(x) cos(x) dx = 19∫ u⁴ du . in terms of u, we get c, which, in terms of sin(x), becomes c.

Answer 1

Using the substitution u = sin(x), we can simplify the integral ∫19 sin^4(x) cos(x) dx to 19∫ u^4 du. By integrating and substituting back, we can express the final answer in terms of sin(x).

Step-by-step explanation:

In this problem, we are given the integral ∫19 sin^4(x) cos(x) dx and are asked to simplify it using the substitution u = sin(x). By substituting u for sin(x), we can rewrite the integral as 19∫ u^4 du.

Integrate this expression to find c, and then substitute back to express the final answer in terms of sin(x).