Question

Find ∫sin (πx/2)

Answer 1

what does sin integrate to?

Answer 2

-cos

Answer 3

then we know this at least has to come from -cos(pi x/2) taket he derivative of that to see what we need to include.

Answer 4

Theres my problem we get sin(pix/2) times (pi/2)

Answer 5

So I need something that cancles out the (pi/2)

Answer 6

then we need to find a pi/2 to attach to our integral so that we have exactly that :)

Answer 7

does 2/pi cancel out pi/2?

Answer 8

Yeah

Answer 9

then lets us that :)

Answer 10

\[\frac{d}{dx}[-\frac{2}{pi}cos(\frac{pi}{2}x)]\to\ \frac{2pi}{2pi}sin(\frac{pi}{2}x)\]

Answer 11

Thank you, I have to admit that was fun

Answer 12

lol :)

Answer 13

when the problems arent so basic, they use something called a u-sub technique to clean things up

Answer 14

\[\int sin(pix/2)dx\]
\[pix/2 = u\]
\[\frac{d}{dx}[pix/2 = u]\to\ \frac{dx}{dx}pi/2 = \frac{du}{dx}\]
\[dx=\frac{2}{pi}du\]

substitute the parts now

\[\int sin(pix/2)dx\]\[\int sin(u)\frac{2}{pi}du\to\ \frac{2}{pi} \int sin(u)du\]

Answer 15

o ok I didnt think to use the u sub when I was looking at it

Answer 16

i did, but felt it rather pointless :) when they are this basic, you need to develop a foresight