Question

Calculus Help! U-substitution

Answer 1

what do you propose for a u?

Answer 2

i tried it with U=x^2 and went through the problem but most likely my algebra was off somewhere

Answer 3

most likely :)

u = x^2 is appropriate

Answer 4

try this thought ... what would you assume would be a likely function that this was derived from?

Answer 5

quick question, am i able to pull that -7 out in front of the integral or is it stuck there with the x? and this seems to be derived from -sin(x)

Answer 6

its a constant, we can use it or abuse it ... either way

Answer 7

-cos comes from -sin

assume some function: -k sin(x^2)

the derivative is therefore: -2k x cos(x^2)

Answer 8

what is k? -2k = -7

Answer 9

so then it should end up with 7/2sin(x^2) and then just plug in my limits of integration

Answer 10

u subbing of course is just finding a way to work this out into a more familiar setup ...

u = x^2; du = 2x dx

-7x cos(x^2) dx

-7/2 cos(x^2) 2x dx

-7/2 cos(u) du

Answer 11

-7/2 sin(u) yes

Answer 12

ok so the negatives don't cancel?

Answer 13

ahh thats where i messed up i made it a positive 7/2sin(x^2)

Answer 14

\[\int-7xcos(x^2)~dx=-\frac72sin(x^2)\]
\[-\frac72[sin(\pi)-sin(0)]\]

Answer 15

got it! thank you so much i have a few more I'm stuck on so stay tuned

Answer 16

if the site behaves itself ... and my dementia doesnt set in ... maybe