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## Homework Statement

Sketch the region defined by: y ≤ x^2 and 4 ≥ y ≥ 0 and y ≥ 2x − 4. Evaluate the area defined by the above inequalities.

## Homework Equations

## The Attempt at a Solution

I have already plotted the positive part and found the area. However, the negative part seems to be infinite. I am required to find the area, surely it's not infinite then.

The area under x^2 in the negative part, above 0, below 4 and above the line is an infinite rectangle starting from x=-2 and stretching to negative infinity. What am I doing wrong?

Here's a diagram: http://www.quickmath.com/webMathematica3/quickmath/graphs/inequalities/advanced.jsp#c=plot_advancedgraphinequalities&v1=y<x^2&v2=y>0&v3=y<4&v4=y>+2x-4&v7=x&v8=y&v9=-10&v10=10&v11=-6&v12=6