Question

How do I approach this:

integral of sin(pi x)cos(pi x) dx?

Answer 1

u sub

Answer 2

\[=\int\limits_{ }^{}\cos(\nu x) d(\sin(\nu x) *1/\nu=...\]

Answer 3

suppose to be: pi*x...
something wrong with my table :)

Answer 4

I tried u = sin(pi x) and came up with 1/2 sin^2 (pi x) +c ?

Answer 5

should be 1/(2pi)

Answer 6

Let\[u =\sin (\pi x) dx\]\[du/\pi =\cos (\pi x) dx\]

Answer 7

right... so your answer should have 1/2pi
not just 1/2
right?

Answer 8

I am not sure what you guys are referring to 1/2 and sin^2?!

Answer 9

Oh, you mean, after the integration.

Answer 10

\[(\pi/2)\sin ^{2}(\pi x)\]

Answer 11

Ok the answer is (1/2pi)*sin^2 (pi x) +C

Please verify as i feel that its still not right.

Thankyou

Answer 12

You have to say what you think is wrong. I showed the basics of the works.

Answer 13

Actually it should be\[(1/2\pi)\sin ^{2}(\pi x) + C\]

Answer 14

Thank you.