- #1
swashbuckler77
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My Calc II class is currently doing Calc I integration review before we get started with integration by parts. I am using an online system that gives immediate feedback on my work and it has said that my answer is wrong. Not sure where I'm going wrong.
Evaluate: [tex]\int \frac{(t+9)^2}{t^3} dx[/tex]
Sum rule: [tex]\int (f + g) dx = \int (f) dx + \int (g) dx[/tex]
Common denominator rule: [tex]\frac{(a+b)}{c} = \frac{a}{c} + \frac{b}{c}[/tex]
1. Multiply out the numerator
[tex](t+9)^2[/tex]
[tex]t^2 + 18t + 81[/tex]
2. Result
[tex]= \int \frac{t^2 + 18t + 81}{t^3} dx[/tex]
3. Split up into three fractions by the common denominator rule provided
[tex]= \int ( \frac{t^2}{t^3} + \frac{18t}{t^3} + \frac{81}{t^3} ) dx[/tex]
4. Simplify
[tex]= \int ( \frac{1}{t} + \frac{18}{t^2} + \frac{81}{t^3} ) dx[/tex]
5. By the Sum Rule, I can rewrite the integral as follows
[tex]= \int \frac{1}{t} dx + \int \frac{18}{t^2} dx + \int \frac{81}{t^3} dx[/tex]
6. Integrate each part
[tex]= ln(t) - \frac{18}{t} - \frac{81}{2t^2} + c[/tex]
7. My final answer
[tex]\int \frac{(t+9)^2}{t^3} dx = ln(t) - \frac{18}{t} - \frac{81}{2t^2} + c[/tex]
Homework Statement
Evaluate: [tex]\int \frac{(t+9)^2}{t^3} dx[/tex]
Homework Equations
Sum rule: [tex]\int (f + g) dx = \int (f) dx + \int (g) dx[/tex]
Common denominator rule: [tex]\frac{(a+b)}{c} = \frac{a}{c} + \frac{b}{c}[/tex]
The Attempt at a Solution
1. Multiply out the numerator
[tex](t+9)^2[/tex]
[tex]t^2 + 18t + 81[/tex]
2. Result
[tex]= \int \frac{t^2 + 18t + 81}{t^3} dx[/tex]
3. Split up into three fractions by the common denominator rule provided
[tex]= \int ( \frac{t^2}{t^3} + \frac{18t}{t^3} + \frac{81}{t^3} ) dx[/tex]
4. Simplify
[tex]= \int ( \frac{1}{t} + \frac{18}{t^2} + \frac{81}{t^3} ) dx[/tex]
5. By the Sum Rule, I can rewrite the integral as follows
[tex]= \int \frac{1}{t} dx + \int \frac{18}{t^2} dx + \int \frac{81}{t^3} dx[/tex]
6. Integrate each part
[tex]= ln(t) - \frac{18}{t} - \frac{81}{2t^2} + c[/tex]
7. My final answer
[tex]\int \frac{(t+9)^2}{t^3} dx = ln(t) - \frac{18}{t} - \frac{81}{2t^2} + c[/tex]