Question 22 of 25
What are the new limits of integration if apply the substitution $u = 6 x + π$ to the integral $\int_{0}^{π} \sin (6 x + π) d x$ ?
(Express numbers in exact form. Use symbolic notation and fractions where needed.)
lower limit:
upper limit:

Answer

Expert–verified

Hide Steps

Answer

The new limits of integration are $π$ and $7 π$ .

Steps

Step 1 ：Apply the substitution $u = 6 x + π$ to the integral $\int_{0}^{π} \sin (6 x + π) d x$ .

Step 2 ：Substitute the lower limit of integration $x = 0$ into $u = 6 x + π$ to get the new lower limit. This gives $u = π$ .

Step 3 ：Substitute the upper limit of integration $x = π$ into $u = 6 x + π$ to get the new upper limit. This gives $u = 7 π$ .

Step 4 ：The new limits of integration are $π$ and $7 π$ .