`y = 12 - x^2, y = x^2 - 6` Sketch the region enclosed by the given curves and find its area.

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`y=12-x^2 , y=x^2-6`

Refer the attached image. Graph of y=12-x^2 is plotted in blue color and graph of y=x^2-6 is plotted in red color. The curves intersects at x=`+-` 3

Area of the region enclosed by the given curves A=`int_(-3)^3((12-x^2)-(x^2-6))dx`

`A=int_(-3)^3(12-x^2-x^2+6)dx`

`A=2int_0^3(18-2x^2)dx`

`A=2[18x-2x^3/3]_0^3`

`A=2(18*3-2/3(3^3))`

`A=2(54-54/3)`

`A=2(108/3)`

`A=72`

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`y=12-x^2 , y=x^2-6`

Refer the attached image. Graph of y=12-x^2 is plotted in blue color and graph of y=x^2-6 is plotted in red color. The curves intersects at x=`+-` 3

Area of the region enclosed by the given curves A=`int_(-3)^3((12-x^2)-(x^2-6))dx`

`A=int_(-3)^3(12-x^2-x^2+6)dx`

`A=2int_0^3(18-2x^2)dx`

`A=2[18x-2x^3/3]_0^3`

`A=2(18*3-2/3(3^3))`

`A=2(54-54/3)`

`A=2(108/3)`

`A=72`

 

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