Find area

y=6-x^2 and y=x+4

find Area under any curve = ∫ydx for range of x considered for the limits.

Expert Solution

Intersection points of these two curves are found by solving as simultaneous equations.

y=6-x^2=x+4

x^2+x-2=0

x= -2 or 1

required area

= ∫(6-x^2)dx-∫(x+4)dx

=6x-x^3/3 -x^2/2-4x for limits x -2 to 1

=-x^3/3 -x^2/2+2x for limits x -2 to 1

=-((-2)^3-(1)^3)/3 -((-2)^2-(1)^2)/2+2(-2-1))

=3-1.5-6

=-4.5 sq units

Modulus 4.5 sq units

4.5 unit²

Nipun Maity answered 2 years ago

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