Question

if the substitution u=sqrt(x+1) is used, then dx/(xsqrt(x+1)) on the interval [0,3] is equivalent to...

Answer 1

1/2sqrt(x+1)

Answer 2

\[\rm u = \sqrt{x+1} \implies du = \frac{1}{2\sqrt{x+1} }dx \implies \bbox[border:2px solid green]{2du = \frac{1}{\sqrt{x+1}}dx}\]

Answer 3

so you can replace dx/sqrt(x+1) wid 2du

what about x ?

Answer 4

idk what to do with the remaining x

Answer 5

the goal is to replace everything with \(\rm u\)'s

Answer 6

u^2-1?

Answer 7

Yes!

Answer 8

plug them in

Answer 9

so then it is \[2\int\limits u ^{2}-1 du\]

Answer 10

x is in bottom right ?

Answer 11

actually \[\int\limits \frac{ 2du }{ u ^{2}}\]

Answer 12

-1

Answer 13

on interval 2,1

Answer 14

thank you!

Answer 15

that's all i need to do for the answer

Answer 16

interval doesnt look correct

Answer 17

how did u get 2,1 ?

Answer 18

subbed 3 and 0 into sqrt(x+1)

Answer 19

Oh right !

Answer 20

:)

Answer 21

\[\rm \int\limits_1^2 \dfrac{2du}{u^2-1}\]