d92292
find the area enclosed between the curve y=x^3 and the line y=x



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did you sketch the region?

d92292
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im not sure on how to

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you're not sure how to sketch x^3 ?

d92292
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no i mean i sketched it, i dont know what to do after

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say, for example, you're asking about the area enclosed for positive values of x..:
dw:1355190249043:dw

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you can see that it's the area under the line x (from 0 to 1) minus the area under x^3 (from 0 to 1)

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aka:\[\int\limits_{0}^{1} xx ^{3} dx\]

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can you evaluate that integral?

d92292
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and then how do we find the anti derivitve of that
hat

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the usual way:\[\int\limits_{ }^{ } x^n dx = \frac{ x^{n+1} }{ n+1 }\]

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so for \[\int\limits_{ }^{} x^1 dx\]
\[\int\limits_{ }^{} x^1 dx = \frac{ x^{1+1} }{ 1+1}\]

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try it for x^3...

d92292
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x^4/4

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yes

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so \[\frac{ x^2 }{ 2 } \frac{ x^4 }{4 } \]

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ok?

d92292
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and whats next?

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plug in the limts

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for the region on the interval x =0...+inf
( 1/2 1/4 )  (0/2 0/4)

d92292
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kk