Question

find the area lying between the parabola y=x^2 and the line
x+y-z=0 .​

Answer 1

Answer:

Intersection points

x+2=y , y=x

2

⇒ x

2

−x−2=0

⇒ x=(2,1) , y=(4,1)

Area between curves=Area under ABCEA-Area under ABOA -Area under OCEO

⇒ 3×1+

2

1

=3×3−∫

−1

0

x

2

dx−∫

0

2

x

2

dx

=3+

2

9

−[

3

x

3

]

−1

0

−[

3

x

3

]

0

2

=3+

2

9

−

3

1

−

3

8

=

2

9

units