Question

find the area enclosed by the curve y=3x^2, x-axis and the ordinates x=1, x=3​

Answer 1

Step-by-step explanation:

hope it helps you ❤....

Answer 2

We need to recall the concept of definite integral.

• If $y=f(x)$ is the equation of the curve, then the area under the curve from $x=a$ to $x=b$ is:
• $A=\int\limits^b_a {f(x)} \, dx$

Given:

Equation of the curve is:  $y=3x^2$

Using the definite integral, we get

The area enclosed by curve is,

$Area=\int\limits^3_1 {3x^2} \, dx$

$Area=[\frac{3x^3}{3} ]_1^3$

$Area=[x^3]_1^3$

$Area=3^3-1^3$

$Area=27-1$

$Area=26$

Hence, the area enclosed by the curve, x-axis and the ordinates $x=1$,$x=3$ ​is $26$ sq. units.