Find the area enclosed by the given curves.
-$$y = x ^ { 3 } , y = 4 x$$
A) 16
B) 4
C) 8
D) 2

Question

Quizplus · Accepted Answer

To find the area between the curves, we need to find their intersection points first.
$$x^3 = 4x$$
$$x(x^2-4)=0$$
$$x=0, x=2.$$
Now we need to integrate the difference between the curves with respect to x, from 0 to 2:
$$\int_{0}^{2}(4x-x^3) dx=\left[2 x^2-\frac{x^4}{4}\right]_0^2=8-\frac{8}{4}=8-2=6.$$
Therefore, the area enclosed by the curves is 6 square units, which is closest to option C (8).

Find the Area Enclosed by the Given Curves y=x3,y=4xy = x ^ { 3 } , y = 4 xy=x3,y=4x

Find the Area Enclosed by the Given Curves $y = x ^ { 3 } , y = 4 x$