Which definite integral would you use to compute the area enclosed by the parabola y=-x^2+4 and the line y=2x-3?

1 Answer
Jun 1, 2018

color(blue)[A=int_(-3.828)^(1.828)(-x^2-2x+7)*dx

Explanation:

the area Between two curves due to "x-axis" given by:

color(red)[A=int_a^by_2-y_1*dx

where y_2 is the curve in the top and y_1 is the curve bottom.

in your question the area between the curves is given by:

color(blue)[A=int_(-3.828)^(1.828)(-x^2+4)-(2x-3)*dx

color(blue)[A=int_(-3.828)^(1.828)(-x^2-2x+7)*dx

show the figure below the area between the two curves:

jamesjames

to find the cross between the curve :

y_2=y_1

-x^2+4=2x-3

x^2+2x-7=0

After solving it you will get:

x=-3.828 or x=1.828