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  • Using integration, find the area of the following region. {(x, y):lx-11≤ y ≤5-x2)

Using integration, find the area of the following region. {(x, y):lx-11≤ y ≤5-x2)

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Region given:

\left\{(x, y):|x-1| \leq y \leq 5-x^2\right\}

Lower boundary : y=|x-1|

Upper boundary: y=5-x^2

We have to find the points of intersection of the curves y=|x-1| \text { and } y=5-x^2 now

For x \geq 1,|x-1|=x-1

Set x-1=5-x^2

We have x^2+x-6=0

Now, upon factoring : (x+3)(x-2)=0

Therefore, x=-3 \text { or } x=2

Since, x \geq 1,

Therefore, the curves intersect at x=2

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Divya Sharma

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