Finding area bounded by x axis, x=0, and x=5

[tjohn101]

Homework Statement

I have a problem where the graph of the equation is below the x-axis at x=0, crosses the x-axis at x=2, and is above at x=5. To find the area of this would I just split the interval into two parts, find both areas, and then add them? Or would I simply ignore the part of the graph that is below the x axis? "Bounded by the x axis" confuses me and that is why I am unsure.

Homework Equations

The Attempt at a Solution

 

[malicx]

Homework Statement

I have a problem where the graph of the equation is below the x-axis at x=0, crosses the x-axis at x=2, and is above at x=5. To find the area of this would I just split the interval into two parts, find both areas, and then add them? Or would I simply ignore the part of the graph that is below the x axis? "Bounded by the x axis" confuses me and that is why I am unsure.

Since area is a positive quantity, you will want to find the negative part and positive part separately, make them both positive, and then add them. Imagine if you had a larger negative area than positive, then you would have a negative area!

On the other hand, if you are required only to evaluate the integral (not find the area of the integral), you would not have to split the regions up.

 

[tiny-tim]

Hi tjohn101!

You haven't actually given us the whole sentence …

presumably it includes words something like "and the graph" …

but what words exactly, and how are they joined to the rest of the conditions?

(if it says "Find the area bounded by the graph, the x axis, x=0, and x=5", then as malicx says, both areas are positive, and you add them)