Question

Find the area of the region bounded by the curves y=6-x*2and . y=x=4

Answer 1

Answer:

y=6-x*2 y=x=4

given 6-x =6 +1=5

given y=x=4 -5.5= 6+4=2 I think it is helpful so

Answer 2

Answer:

Step-by-step explanation

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

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(Answer)