Question

`int_2^7 sqrt(x)/(sqrt(x) + sqrt(9 - x))  dx` = ______.

Options

• `7/2`

• `5/2`

• 7

• 2

Answer 1

`int_2^7 sqrt(x)/(sqrt(x) + sqrt(9 - x))`  dx` = bbunderline(5/2)`

Explanation:

Let

`int_2^7 sqrt(x)/(sqrt(x) + sqrt(9 - x))`  dx

Using the substitution u = 9 − x, we find that the integral transforms to

`int_2^7 sqrt(9 - x)/(sqrt(x) + sqrt(9 - x))`  dx

Adding these two expressions gives

2I = `int_2^7 1 dx` 

2I = 7 − 2

2I = 5

∴ I = `5/2`