To evaluate ∫ 3x2 cos (2x3 - 4) dx, it is necessary to let a. u = 6x. b. u = 6x2 c. u = 2x3 -4 d. u = 3x2

The correct answer is C, to let u = 2x^3 - 4.
This allows du = 6x^2 dx, and the integral will become:
integral of (1/2)(du) cos(u), which can be integrated in a straightforward manner.
The rule of thumb is to set the entire expression of the trigonometric function as a single variable if possible, to make it simpler.

When rates are expressed as a quantity of 1, such as 2 feet per second or 5 miles per hour, they are called unit rates. if you have a multiple-unit rate such as 120 students for every 3 buses, and want to find the single-unit rate, write a ratio equal to the multiple-unit rate with 1 as the second term.