Question

To evaluate ∫ 3x2 cos (2x3 - 4) dx, it is necessary to let A. u = 2x3 -4 B. u = 3x2 C. u = 6x. D. u = 6x2

Answer 1

When integrating, u-substitution is used to make things easier to work out. In u-substitution, the "u" is generally determined if its derivative is in the expression. That way when integrating with respect to "u", you can just replace the derivative of the u with "du" and easily integrate.

For this question, it would be easiest to let:

`u=2x^3`

Let's take the derivative of u and see if we can work something out:

`du = 6x^2`

We have an x² in the integral expression, and therefore, it's valid for us to let u = 2x³. Thus, your answer is A.