Question

Can someone explain to me how to use u-sub to definite integrals.
im confused because my teacher says to change a and b by pluging them into the u equation to get a new a and b. but when i do that i get the wrong answer. and when i just keep the same a and b i get it correct.

Answer 1

post an example

Answer 2

\[\int\limits_{0}^{1}(2x-3)^3dx\]
for this one i did normal and got the right answer.
All i did was u and got du multiplied by one half then plged in to get F(1)-F(0)

My teacher though did this one in class
\[\int\limits_{-5}^{0}x \sqrt{4-x}dx\]
he got u=4-x and then coverted the x to u.
and then he did the anti derivative but then pluged in the a and b into the u to get new a and b so the 0 changed to 4 and - 5 changed to 9.


My question is how was i able to get the right answer without changeing a and b for the first one? when i do the first problem the way the second one is done i get the wrong answer

Answer 3

@optiquest

Answer 4

did you ever change the limits of integration when you u subbed

Answer 5

theres two different ways people do u sub

Answer 6

what i did on the first one is basically just kept the integral the same and just tried looking for the anti derivative.

Answer 7

When do we change the limits?

Answer 8

thqtw the part im stuck on bcause i didnt know you have to do that i just get my pencil find anto derivatives and plug in the numbers

Answer 9

after you determine the new u and du you have to find the new limits

Answer 10

if you dont do it that way you have to keep the same limits and replace u with what you had originally after you take the integral

Answer 11

yes thats what i do replace u with what u equals then add the regular limit

Answer 12

oh jesus christ i see what my teacher did lol oh jesus christ when you get what u equals you dont change it back to x. lol thank you!