AP / AB Calculus Test - Sample Questions 17 & 18

[patrickjmt]

yes, you change limits of integration when you change the variable (ie, u substitution)

[patrickjmt]

that is the hard part about integration, it is sometimes not obvious what to do.

if i see something that is the derivative of something else (in the integrand), then u sub often is the trick to use

[patrickjmt]

you say:

It's best to change the limits to U-limits as well and not to resub back in for u and use the original limits

that is up for debate i think! it is all the same to me...

however, it is notationally incorrect to do a u-sub and use the original limits; it is just not right anymore! you can always revert back to the original limits.

in regards to the 1/(b-a) this is just a constant, so all the substitutions in the world will not change its value!

[patrickjmt]

@reighteeen i am probably not the mostest stupidest person in the wurld at least

[reighteeen]

you probably get this a lot but you're freakin' smart!

[sujkrish]

@cyborg939, it is F(5)-F(1)/b-a, please note the capital letters used.

[luckystarlover]

how do you know when you have to do U substitution

[quynhho]

So when exactly do you have to change the limits of integration? Is it every time you use u substition?

[cyborg]

Why don't you do f(5)-f(1)/(5-1)? Isn't that the average value theorem? In this case, it does produce a different answer. The formula you used is the mean value theorem. Is there a difference and how do you choose which formula to use?

[almonte]

do you know how to do calc bc(or the second level of calc)

[Bloodsaberxy]

you friends with Sal? you guys are awesome

[BakaDemi]

i would not substitute, just FOIL the function out and simplify it, then integrate it normally.

[supergsx]

It's usually useless to use u substitution when the derivative of u is just 1

[xxGATEZxx]

it didnt matter because he made the limits 4 and 0, so if he had subsituted x-1 back in and left his limits 5 and 1, you would too be evaluating between 0 and 4 it didnt matter

[JustSemantics]

Would this be the same as integrating the function x^2 over the interval [0, 4]? because that seems like it'd be much less trouble : P

[tRENtCAE]

Could you please do the college board 2012 ones?!? Thanks for the help with these ones

[MikhailFederov]

I've known how to do this, but after watching something hit me: It's best to change the limits to U-limits as well and not to resub back in for u and use the original limits. But what about the original 1/(b-a) in the beginning? Should those also have to be changed?

[billybobvvify]

Didn't you forget to replace your u with x-1 at the end?

[KuuhakuBlank]

Why am i here? I'm only in Algebra 2