Use a definite integral to find the area of the

Ответ:

tori829

01.02.2022

Given :

Given a curve , y=2x^2 .

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 :

$A=\int\limits^b_0 {2x^2} \, dx \\\\A= |_0^b(\dfrac{2}{3}x^{(2+1)})\\\\A=\dfrac{2b^3}{3}$

( Integration of x^2 is $\dfrac{x^3}{3}$ )

Therefore , the region between the given curve and the x-axis on the interval [0, b] is $\dfrac{2b^3}{3}$ .

Hence , this is the required solution .

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fgcherubin

18.05.2020

(A) is the correct answer

Step-by-step explanation:

1/6 stays the same but 3/5 canges to 5/3

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