Definite integral of a negative function?

Question

What is calculated by the definite integral if the function is negative for every value between the points a and b?

Answer 1

I hope I understood the statement of the problem correctly.
You are asking for a set of conditions when an area will be negative.

1. Let f(x)<0 then the area must lie in the positive x domain (x>0).
2. Let f(x)>0 the area must lie in the negative x domain (x<0).

Answer 2

You would probably be calculating a number, which does not necessarily mean area(though it does give you the value of the area under the x axis), it depends on its uses. But if you are calculating area, you should put the integral under absoulte value bars unless you know that the reason why the integral gave anegative number was because the function was under the x axis. -Sorry if you needed more info., I just typed this really fast with what I quickly remebered-

Answer 3

it is not wrong to get definite integral negative.....since the area under curve is just the magnitude of the value obtained, but u must be carful in cases where the function moves from + to - or vivce versa, in such cases you will have find the point where the change occurs and split the definite intehral into 2 parts, one from sa y a to c and c to b.

Answer 4

Area above the function to the zero line. Would be a negative result.

Answer 5

The area, below the independent variable (iv) axis, bounded by the function between iv =a and iv=b and the iv axis. The function is, say, f(iv). So we are plotting iv on the horizontal axis and f(iv) on the vertical axis, assuming that we are talking about a 2D situation.

Answer 6

area under x axis.

function will be there negative
but the area can not be negative.

If it is negative find absolute value of it.