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

Find the area bounded by the curve [tex]y=x^2-2[/tex], the y-axis, y=0 and y=1

I got an answer, but when I checked it using graphmatica, it was wrong (also the result is logically too large). I cannot see where I went wrong though, so could someone please help me spot the mistake.

2. Relevant equations

[tex]\int_{a}^{b}f(y)dy = \left [ F(y) \right ]_{a}^{b}[/tex]

[tex]\int_{a}^{b}(ax+b)^ndx=\left [ \frac{(ax+b)^{n+1}}{a(n+1)}\right ]_a^b[/tex]

3. The attempt at a solution

[tex]A=\int_{0}^{1}xdy[/tex]

where [tex]x=\pm \sqrt{y+2}[/tex]

thus,

[tex]A=\int_{0}^{1}\pm \sqrt{y+2}.dy[/tex]

[tex]A=2\int_{0}^{1}\sqrt{y+2}.dy[/tex]

[tex]=2 \left[ \frac{(y+2)^{3/2}}{3/2} \right]_0^1[/tex]

[tex]=2\left( \frac{3^{3/2}}{3/2} \right)[/tex]

[tex]=4\sqrt{3}.u^2[/tex]

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# Homework Help: Simple definite integral

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