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Question
Evaluate : `int_1^9(x + 1)/sqrt(x)*dx`
Solution
`int_1^9(x + 1)/sqrt(x)*dx = int_1^9(x/sqrt(x) + 1/sqrt(x))*dx`
= `int_1^9 x^(1/2)*dx + int_1^9 x^(-1/2)*dx`
= `[(x^(3/2))/(3/2)]_1^9 + [(x^(1/2))/(1/2)]_1^9`
= `(2)/(3)[9^(3/2) - 1^(3/2)] + 2[9^(1/2) - 1^(1/2)]`
= `(2)/(3)[(3^2)^(3/2) - 1] + 2[3 - 1]]`
= `(2)/(3)[27 - 1] + 4`
= `(52)/(3) + 4`
= `(64)/(3)`.
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