Question

the integral of sin(pi t) cos(pi t) dt

Answer 1

sinpitcospit = 1/2 * (sin2t)
i guess u can do the final step..!!! gud luck

Answer 2

I do not understand how you got there.

Answer 3

2sinpitcospit = sin2t , n its an formula

Answer 4

and some how the answer is suppose to be 1/2pi sin^2pit + c

Answer 5

use ur mind a little bit... wish u luck! i guess its easy to figure that

Answer 6

ok... so have you seen the trig identity

sin(2x) ...?

Answer 7

no I have not

Answer 8

ok... have you seen

sin(a + b)..?

Answer 9

or something of that form... A + B, x + y..?

Answer 10

I do not remember

Answer 11

sinhx = -coshx

Answer 12

ok so a common trig identity is

sin(2x) = 2sin(x)cos(x)

which is starting to look a lot like you have in your problem...

does that make sense...?

Answer 13

okay, yes

Answer 14

don't worry about hyperbolic functions..

Answer 15

so if you halved both sides of the equation you get

1/2 sin(2x) = sin(x)cos(x)

does that make sense...?

Answer 16

yes because the 2 cancels out with the 1/2 right?

Answer 17

correct... so you problem, with a little substitution can be written as

\[\int\limits \sin(\pi t)\cos(\pi t) dt = \int\limits \frac{1}{2} \sin(2\pi t) dt = \frac{1}{2} \int\limits \sin(2\pi t) dt\]

so you can integrate from here...

Answer 18

u sub works too :)

Answer 19

give me a sec, trying to understand this

Answer 20

sin(pi t) cos(pi t) dt
pi cos(pi t ) is derivative of sin(pi t)

Answer 21

so....

Answer 22

there you go, lots of people to help, good luck with it