Question

The area bounded by the linesx= 0, y = 1 and y=x using double integration is​

Answer 1

Answer:

∫

0

a

[(x+2)−x

2

]dx

First we need to get

′

a

′

This represent the point of intersection of the two curves, so we equate the two functions:

x+2=x

2

⇒x

2

−x−2=0

⇒x

2

−2x+x−2=0

⇒(x−2)(x+1)=0

Since, x>0, we reject the solution x=−1

Hence,a=2

So:A=∫

0

2

[(x+2)−x

2

]dx

=[

2

x

2

+2x−

3

x

3

]

0

2

=2+4−

3

8

=

3

10