Integration Problem 1 Solution: Calculating ∫(√x + 1/√x)^2 dx from 4 to 9

[PhizKid]

Homework Statement

\int_{4}^{9} (\sqrt{x} + \frac{1}{\sqrt{x}})^{2} \textrm{ } dx

Homework Equations

The Attempt at a Solution

\int_{4}^{9} (\sqrt{x} + \frac{1}{\sqrt{x}})^{2} \textrm{ } dx \\\\<br /> \int_{4}^{9} (x + 1 + 1 + \frac{1}{x}) \textrm{ } dx \\\\<br /> \frac{x^2}{2} + 2x + ln(x) | \textrm{4 to 9} \\\\<br /> (27 + ln(9)) - (\frac{88}{9} + ln(4)) \\\\<br /> \frac{155}{9} + ln(\frac{9}{4})

The solution says this is incorrect...can anyone correct me where I integrated wrong?

 

[bossman27]

I think you just goofed up when plugging in 9 and 4. Everything up until that point is correct.

 

[Mark44]

Homework Statement

\int_{4}^{9} (\sqrt{x} + \frac{1}{\sqrt{x}})^{2} \textrm{ } dx

Homework Equations

The Attempt at a Solution

\int_{4}^{9} (\sqrt{x} + \frac{1}{\sqrt{x}})^{2} \textrm{ } dx \\\\<br /> \int_{4}^{9} (x + 1 + 1 + \frac{1}{x}) \textrm{ } dx \\\\<br /> \frac{x^2}{2} + 2x + ln(x) | \textrm{4 to 9} \\\\<br /> (27 + ln(9)) - (\frac{88}{9} + ln(4)) \\\\<br /> \frac{155}{9} + ln(\frac{9}{4})

The solution says this is incorrect...can anyone correct me where I integrated wrong?

Your integration was fine. You have a mistake when you evaluate your antiderivative, when x = 4. If x = 4, x²/2 = 16/2, not 88/9.

 

[STEMucator]

Homework Statement

\int_{4}^{9} (\sqrt{x} + \frac{1}{\sqrt{x}})^{2} \textrm{ } dx

Homework Equations

The Attempt at a Solution

\int_{4}^{9} (\sqrt{x} + \frac{1}{\sqrt{x}})^{2} \textrm{ } dx \\\\<br /> \int_{4}^{9} (x + 1 + 1 + \frac{1}{x}) \textrm{ } dx \\\\<br /> \frac{x^2}{2} + 2x + ln(x) | \textrm{4 to 9} \\\\<br /> (27 + ln(9)) - (\frac{88}{9} + ln(4)) \\\\<br /> \frac{155}{9} + ln(\frac{9}{4})

the solution says this is incorrect...can anyone correct me where i integrated wrong?

$9^2 ≠ 27$

In specific : x^2/2 = 81/2