Question

find the area of the region enclosed by the curve y=x^2-3x+2 and the x-axis​

Answer 1

Answer:

Given curve is x

2

−3x+2=0

The roots of this quadratic equation are 1 and 2

Thus, the area under the curve and X-axis and the ordinates x=0 x=3 is

A=∫

0

3

(x

2

−3x+2)

A=∫

0

1

(x

2

−3x+2)−∫

1

2

(x

2

−3x+2)+∫

2

3

(x

2

−3x+2) ....... (Between x=1 to x=2, the curve is below X-axis)

After integrating and substituting upper and lower limits, we get

A=

6

5

+

6

1

+

6

5

∴A=

6

11