Question

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

Answer 1

try giving u substitution a shot

Answer 2

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

Answer 3

Can you do \(\int \sin(x)\;dx\)?

How about \(\int \sin(2x)\;dx\)?

Answer 4

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

Answer 5

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

Answer 6

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

Answer 7

no worries!