Let I=\int_{x-0}^{1} \int_{y-0}^{x^{2}} x y^{2} d y d x . Then, I may also be expressed as

Correct Answer is : ∫y−01∫x−y1xy2dxdy

\int_{y-0}^{1} \int_{x-0}^\sqrt{y} y x^{2} d x d y

\int_{y-0}^{1} \int_{x-0}^\sqrt{y} x y^{2} d x d y

\int_{y-0}^{1} \int_{x-\sqrt{y}^{1} x y^{2} d x d y

\int_{y-0}^{1} \int_{x-\sqrt{y}^{1} y x^{2} d x d y

GATE Mechanical Engineering (ME) 2020 Shift 2 Solved Paper

Question : 19 of 65

Marks: +1, -0

Let

I=∫↙{x-0}↖{1} ∫↙{y-0}^{x^{2}} x y^{2} d y d x .

Then, I may also be expressed as

Solution:

0 ≤ y ≤ x^{2}

(This is represented by vertical stripe)

0 ≤ x ≤ 1

After change of order integration

√{y} ≤ x ≤ 1

0 ≤ y ≤ 1

I=∫↙{y-0}↖{1} ∫↙{x-√{y}}^{1} x y^{2} d x d y

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