Question

How do I solve this integration?

Answer 1

\[\int\limits_{0}^{0,5}12\sin(2\pi t)dt\]

Answer 2

u substitution. let \(u=2\pi t\)

Answer 3

Looks like a u sub..

Let u = \(\large 2 \pi t\) so du = \(\ 2 \pi dt\)
\[\large \frac{12}{2 \pi} \int\limits_{0}^{0.5}\sin(u)du \]
Can you take it from there?

Answer 4

yes, thank you very much!

Answer 5

technically, the limits should change but if you put back in terms of t it will be okay.

Answer 6

^ I was thinking about that...but I always was used to changing them back so I omitted it..good point though @pgpilot326

Answer 7

after integrating...

Answer 8

I still have a question xD

Answer 9

When I solve it should I do it like this?

Answer 10

i do the same thing... sometimes i just write a and b for my limits and then get the integrated functiion in terms of the original variable and then put back the original limits of integration

Answer 11

like what?

Answer 12

\[\frac{ 12 }{ 2 \pi } \int\limits_{0}^{0,5}\sin(u) du\]

Answer 13

oops

Answer 14

so, you don't know how to integrate sin?

Answer 15

?

Answer 16

No, I wanted you to check if I'm doing it correclty!

Answer 17

\[\frac{ 12 }{ 2 \pi }\left[ -\cos(u) \right]_{0}^{0,5}\]

Answer 18

so far, so good

Answer 19

that's it, but again... before you evaulate at the current limits, you need to either change the argument of the cos function or change the limits of integration.

Answer 20

you were evaluating as t went from 0 to 0.5, u will go to different values (well, at least the upper limit will be different).

Answer 21

since u=2 pi t
I will have:
\[\frac{ 12 }{ 2 \pi }\left[ -\cos2 \pi t \right]_{0}^{0,5}\]
and then:
\[\frac{ 12 }{ 2 \pi }\left[ -\cos2 \pi+ \cos(0) \right]\]
Finally:
\[\frac{ 12 }{ 2 \pi }\left[ 1+1 \right]= \frac{ 12 }{ \pi }\]

Answer 22

isn't 2pi*0.5 = pi ?

Answer 23

right answer, wrong execution

Answer 24

\(-\cos\pi = -(-1)=1\)

Answer 25

@phi yes it is, I actually made a mistake while I was writing

Answer 26

@ but the calculations are correct, when I have cos pi I get minus one which eventually becomes one

Answer 27

@pgpilot326 Are you referring to another method or to the calculations?

Answer 28

no worries... good job!

Answer 29

the cos post was in ref to your calcs

Answer 30

Thanks and thank you for helping me out :D

Answer 31

the server seems to be off in how it posts...

are you all good @naylah ?

Answer 32

Yeah I'm ok

Answer 33

Now I have to go, take care!