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