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Question
`int_2^7 sqrt(x)/(sqrt(x) + sqrt(9 - x)) dx` = ______.
Options
`7/2`
`5/2`
7
2
Solution
`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`
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