You are Here: Home >< Maths

Definite Integral of Sin(x) --- is it 4 or 0? watch

1. Very basic question.

What's the definite integral of sin(x) with limits of 0 to 2pi.

Is it 0 or 4?

If the limits are 0 to pi it is 2; and if the limits are from pi to 2pi, then it is -2.

Is the definite integral the sum of the area, in which case the absolute value of -2 is taken, so it adds up to 4, since area is always positive?

Or is the definite integral not the area, but rather:

∫ sin(x)[0, 2π] dx = [cos(2π) - cos(0)] = 1-1 = 0

Also, if I put it in the calculator, it also gives zero, so I'm leaning towards that idea right now.

I'm making a Matlab program that numerically integrates a function, so I want to make sure if I need to keep or remove the ABS from this code:

if mod(n,2) == 0; % if n is even
S_s = (dx/3)*(abs(y_x(a)) + 4*sum (abs(y_x(a+dx:2*dx:b-dx))) + 2*sum(abs(y_x(a+2*dx:2*dx:b-2*dx))));
else % if n is odd
S_s = (dx/3)*(abs(y_x(a)) + 4*sum (abs(y_x(a+dx:2*dx:b-2*dx))) + 2*sum(abs(y_x(a+2*dx:2*dx:b-dx))));
end
Cheers
2. The integral of sin(x) from 0 to 2pi is 0. The area under the curve is 4.
3. (Original post by Bobifier)
The integral of sin(x) from 0 to 2pi is 0. The area under the curve is 4.
Cool.

Related university courses

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: March 28, 2013
Today on TSR

Edexcel C4 Maths Unofficial Markscheme

Find out how you've done here

1,765

students online now

Exam discussions

Poll
Useful resources

Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

How to use LaTex

Writing equations the easy way

Study habits of A* students

Top tips from students who have already aced their exams

Chat with other maths applicants