Question

find the following integral

Answer 1

\[\int\limits_{?}^{?} (3-x)^10 dx\]

Answer 2

the bracket is raised to 10

Answer 3

Make a substitution. Let u = 3 - x, du = -dx, dx = -du

Answer 4

\[u = 3 - x, -du = dx\]\[\int\limits (3-x)^{10}dx \rightarrow - \int\limits u^{10} du = - \frac {u^{11}}{11} + C \rightarrow - \frac {(3-x)^{11}}{11} + C\]

Answer 5

If you wanna make that positive, you can switch the 3 and the x.\[\int\limits\limits (3-x)^{10}dx = \frac {(x-3)^{11}}{11} + C\]