Question

Integrals, integrals, integrals...

Use Substitution formula to evaluate.

see question in comment box ! :)

Answer 1

\[\int\limits_{0}^{1} \frac{ 4x dx}{ \sqrt{4 +2x ^{2}} }\]

Answer 2

what is the substitution formula ?

Answer 3

substitute that

Answer 4

I somehow doubt this is trig sub, sid.

Answer 5

Well, I just assume this is u-substitution, just like before. So what do you think would be the appropriate choise for u?

Answer 6

Wow, how the hell did I spell that choice as choise?! O_o

Answer 7

you read my mind! okay
u = \[\sqrt{4 + 2x ^{2}}\]

Answer 8

Remember, we rarely want to choose a u-substitution that would be a big chain rule. That choice of u will create extra expressions of x that we dont want. Think of it this way, you usually always want u to be the inside of something. Inside of a power, like the (4+cosx)^6 problem from last time, we wanted u = 4+cosx, not the whole thing, inside of a square root, etc.

Answer 9

du =

Answer 10

ok ok!!

Answer 11

so u = 4 +2x^2

Answer 12

Bingo.

Answer 13

du= 4x

Answer 14

du = 4xdx to be more specific :)

Answer 15

i was getting there :)

Answer 16

okay now what ? how many times before I get integrals eeek!!

Answer 17

i know du/u

Answer 18

Well, we have a u and we have an expression for dx
u = 4 + 2x^2
du = 4xdx. That works out perfectly