Use the substitution

u $=$ cos$($x$)$

to transform and then compute the integral

$/3$cos$3($x$)$sin$($x$)$dx$0$

Transform the integral by first writing the integrand and differential only in terms of u$.$

ba

$$

The original lower bound $0$ and upper bound $/3$ are values of x$.$ Use the substitution

u $=$ cos$($x$)$

to find the new bounds, which are values of u$.$

Lower Bound: a $=$

Upper Bound: b $=$

Which expression$($s$)$ below are equal to the original integral? Select all that apply.

$$

$14$

u$4$

$/30$

$$

$14$

u$4$

$1/21$

$$

$14$

cos$4($x$)$

$/30$

$$

$14$

cos$4($x$)$

$1/21$

Discussion point: Discuss the differences between the above expressions with your group.

Compute the integral.

$/3$cos$3($x$)$sin$($x$)$dx$0$

$=$