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Find the area of the region {(x, y): 0<=...

Find the area of the region `{(x, y): 0<=y<=x^2+1,0<=y<=x+1,0<=x<=2}`

Text Solution

Verified by Experts

Let us first sketch the region whose area is to be found out. This region is the intersection of the following regions.

area of the region OTQPO + area of the region TSRQT
so required area is =`int_0^1(x^2+1)dx+int_1^2(x+1)dx`
`(x^3/3+x)_0^1+(x^2/2+x)_1^2`
`(1/3+1)+(4-3/2)`
`4/3+5/2=23/6`sq unit
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