Answered

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Find the area or the region bounded by the curves y = x^3 and y = x.

Find The Area Or The Region Bounded By The Curves Y X3 And Y X class=

Sagot :

wgiven the functions

[tex]y=x^3[/tex][tex]y=x[/tex]

the area of the curve is given by the integral

the limits are defined by

[tex]y1=y2[/tex][tex]x^3=x[/tex][tex]x^3-x=0[/tex][tex]x(x+1)(x-1)=0[/tex][tex]x=0;x=-1;x=1[/tex]

the defined integral for the ara is given by

[tex]A=-\int_{-1}^0x-x^3dx+\int_0^1x-x^3dx[/tex][tex]A=2\int_0^1x-x^3dx[/tex][tex]A=2\lbrack\frac{x^2}{2}-\frac{x^4}{4}\rbrack_0^1[/tex][tex]A=2\lbrack\frac{1^2}{2}-\frac{1^4}{4}\rbrack_^-2\lbrack\frac{0^2}{2}-\frac{0^4}{4}\rbrack[/tex][tex]A=2\lbrack\frac{1^2}{2}-\frac{1^4}{4}\rbrack_^[/tex][tex]A=2*\frac{1}{4}[/tex][tex]A=\frac{2}{4}=\frac{1}{2}[/tex]

A= 1/2= 0.5

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