Question

Consider the parabola y=x^2. The shaded area is

Answer 1

To get the area of the shaded region we use the concept of integration.

From the diagram, the limits of integration are:

x = 0 to x=2

Lets integrate the function :

We get:

x³ / 3

When we substitute the limits we get :

2³/3 = 8/3

Area is thus 8/3 square units

Answer 2

Answer:

$A=\dfrac{8}{3}$

Option 4 is correct.

Explanation:

We are given a parabola with shaded area.

$y=x^2$

For interval, $0\leq x\leq 2$

Area of shaded region, A

$A=\int dA$

$dA=ydx$

where, $y=x^2$

$A=\int_0^2 x^2dx$

$A=\dfrac{x^3}{3}|_0^2$

$A=\dfrac{8}{3}-0$

Hence, The area of the shaded region is 8/3