Use a definite integral to find the area of the region between the given curve and the x-axis on the interval [0, b].y= 2x^2.

Given :

Given a curve , .

To Find :

The area of the region between the given curve and the x-axis on the interval [0, b] .

Solution :

Now , area under the curve is given by :

( Integration of is )

Therefore , the region between the given curve and the x-axis on the interval [0, b] is .

Hence , this is the required solution .

∠cbe and ∠deb are same-side interior angles.

i took the test