Question

find the area under the curve y=x² from x=0 x =3 with x axis​

Answer 1

Step-by-step explanation:

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

Answer 2

concept

area enclosed  under the curve

given

y=x² from x=0, x=3

find

to find the area under the curve

solution

0∫3  x²×dx

[x³÷3] integrating limit 0 to 3

now area enclosed under the curve

3³÷3-o³÷3=3²

=9 square unit

∴the area under curve is 9 square unit

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