(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find the total area of the region enclosed by the curvex = yand the lines^{2/3}x = yandy = -1.

2. The attempt at a solution

I graphedx = yas y=x^{2/3}^{3/2}and y=-x^{3/2}. Then I graphed the lines y=x and y=-1.

I shaded the region in question, which appears off the cuff to have an area slightly larger than one. To find the area exactly I broke the problem up into two integration steps.

1. [tex]\int[/tex] x dx (from x=-1 to x=0) - [tex]\int[/tex] -1 dx (in the same range of x=-1 to x=0)

+

2. [tex]\int[/tex] -1 dx (from x=0 to x=1) - [tex]\int[/tex] -x^{3/2}dx

I keep getting the whole area as 11/10. This seems close enough, seeing as how the area appears to be slightly greater than 1. However, my textbook's answer glossary tells me that the correct answer is actually 6/5. Can anyone tell me what i'm doing wrong?

I attached a relevant graph (I did it in mspaint, lol, sorry). y=+x^{2/3}is left out of the graph because it is irrelevant. The shaded region, i'm assuming, is the area in question:

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# Homework Help: Find the area enclosed by a curve and two lines.

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