Integrate from 0 to 1 sin(pix)dx
Answer: 2/pi
Please show the work on how to get the answer.

Question

Integrate from 0 to 1 sin(pix)dx
Answer: 2/pi
Please show the work on how to get the answer.

anonymous · Answer

try giving u substitution a shot

anonymous · Answer

should i make my u pix or just x and bring pi out to the front?

tkhunny · Answer

Can you do $\int \sin(x)\;dx$?

How about $\int \sin(2x)\;dx$?

anonymous · Answer

i integrated it and got pi(-cosx) from 0 to 1.  how would i find cos(1) without using a calculator?

anonymous · Answer

so if you choose your u to be pi*x, then du = pi*dx
therefore du/pi = dx
then evaluate the integral with u, then either change your bounds or re substitute in pi*x for your u

anonymous · Answer

oh that's what i forgot! i didn't put my coordinates in terms of u x0 thanks!

anonymous · Answer

no worries!