Evaluate the following integral:

Let ......equation 1

Put

2 – x = y²

Differentiating both sides

– dx = 2ydy

For x = 2

2 – x = y²

2 – 2 = y²

y = 0

For x = 0

2 – x = y²

2 – 0 = y²

y = √2

Substituting the values in equation 1

We know b and a being the upper and lower limits respectively

thus

[

Solving this we get

[

[

[

Thus

[