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Question
Find `int_2^8 sqrt(10 - x)/(sqrt(x) + sqrt(10 - x)) "d"x`
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Solution
We have I = `int_2^8 sqrt(10 - x)/(sqrt(x) + sqrt(10 - x)) "d"x` .....(1)
= `int_2^8 sqrt(10 - (10 - x))/(sqrt(10 - x) + sqrt(10 - (10 - x)) "d"x` .....By (P3)
⇒ I = `int_2^8 sqrt(x)/(sqrt(10 - x) + sqrt(x)) "d"x` ....(2)
Adding (1) and (2), we get
2I = `int_2^8 1"d"x = 8 - ` = 6
Hence I = 3
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