Problem 50
In Exercises 47-52, verify the integration formula.
\(\int u^{n} \cos u d u=u^{n} \sin u-n \int u^{n-1} \sin u d u\)
Text Transcription:
int u^{n} cos u du = u^n sin u - n int u^{n - 1} sin u du
Step-by-Step Solution:
Step 1 of 5) The formula evaluates the line integral on the left side correctly no matter what parametrization is used, as long as the parametrization is smooth. Note that the parameter t defines a direction along the path. The starting point on C is the position r(a) and movement along the path is in the direction of increasing t (see Figure 15.1).
Step 2 of 2
