Calculus - 1 more areas

62

Lokesh Verma ·2010-07-06 10:38:01

here y = Â±(a^2/3-x^2/3)^3/2

So area will be 2âˆ«(a^2/3-x^2/3)^3/2

Now the limit of integral will be from -a to +a

bcos |x| cannot be greater than a (why?)

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tormented ·2010-07-06 11:24:14

Is it because the area becomes negative?

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62

Lokesh Verma ·2010-07-06 11:30:21

no...

but because x^2/3 is always.......

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tormented ·2010-07-06 11:47:12

positive?

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Lokesh Verma ·2010-07-06 11:48:45

yup :)

now think why a circle x²+y²=1 lies within -1, 1?

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tormented ·2010-07-06 11:53:51

is it because the radius is 1? and its centre is origin?

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Lokesh Verma ·2010-07-06 11:55:39

arrey yaar..

y²=1-x² (since x² is +ve ... so y²<1)

Same logic ony 2 gets replaced by 2/3

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tormented ·2010-07-06 11:59:26

Oh yeah but even mine is right na

general eq. of circle is x²+y²+2gx+2fy+c=0

now comparing with your eq. g,f=(0,0) (centre is orgin)
and radius is 1
and so circle lies on -1 and 1

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