Question

The region D enclosed by the lines y = x,y = 0, x = 1 is given by​

Answer 1

Answer:

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Answer 2

Answer:

The region d enclosed by the lines y = x, y = 0, x = 1 is given by $2\int\limits^1_0 {y} \, dx$ and the value of area that comes is 1 Sq. Units.

Step-by-step explanation:

We have the region enclosed by the lines y = x, y = 0, x = 1 and it is asked to get the representation of that area that comes under these lines.

So from the lines the diagram that obtained is attached below.

And from that graph it can be clearly visualise that

Area of region D =

$\int\limits^1_0 {y} \, dx + \int\limits^1_0 {y} \, dx\\=2\int\limits^1_0 {y} \, dx$

But here y = x then the equation can be written as

$2\int\limits^1_0 {y} \, dx=2\int\limits^1_0 {x} \, dx$

⇒$2\int\limits^1_0 {y} \, dx=2[\frac{x^2}{2}]$ runs from 0 to 2

$2\int\limits^1_0 {y} \, dx = 2[1/2 - 0] = 1$

Hence the area of region D enclosed is 1 Sq. Units.