Question

Calculate area bounded by curve y=3x^2- 9 and x-axis between x=2 and x=5

Answer 1

Given that,

Limits x = 2 to x = 5

The given equation is

$y=3x^2-9$

We know that,

The area under a curve between two points can be found by doing a definite integral between the two points.

We need to calculate the area

Using given equation with limits

$\text{Area}=\int_{a}^{b}{y dx}$

Put the value into the formula

$\text{Area}=\int_{2}^{5}{3x^2-9}dx$

On integration

$\text{Area}=(\dfrac{3x^3}{3}-9x)_{2}^{5}$

$\text{Area}=5^3-9\times5-2^3+9\times2$

$\text{Area}=90\ square\ unit$

Hence, The area is 90 square unit.