Find the area below the graph of f, but f is in fractional form?

In summary, the conversation is about finding the area below the graph of a function, specifically f(x) = (2x + 5)/[(x + 2)^2(x + 3)^2] on the interval [0, 1]. The student is struggling with evaluating integrals in fractional form, but is reminded to use partial fractions. They then find a website with a step-by-step guide on solving the problem and are grateful for the help.
  • #1
LilTaru
81
0

Homework Statement



Find the area below the graph of f.

f(x) = (2x + 5)/[(x + 2)2(x + 3)2] xE [0, 1]

Homework Equations



I know the area under the graph is the definite integral with upper limit = 1; lower limit = 0.

The Attempt at a Solution



I have such a hard time evaluating integrals when they are in fractional form. I know if G(x) is the antiderivative of f, then:

Area = G(1) - G(0)

But, I don't know how to find an antiderivative for f? It seems impossible to me! Someone please help!
 
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  • #2
Have you tried partial fractions? They're going to be very useful here.
 
  • #3
We never learned how to use them... Is there a website that shows how to use them?
 
  • #4
Nevermind... Found a website with a similar question and a step-by-step guide of how to solve it and why! It was really helpful! Thanks for putting me on the right track!
 
  • #5
It was no problem. Have a great day!
 

FAQ: Find the area below the graph of f, but f is in fractional form?

What does finding the area below the graph of f in fractional form mean?

Finding the area below the graph of f in fractional form means calculating the total area between the x-axis and the curve of f using fractions or ratios instead of whole numbers.

How is finding the area below the graph of f in fractional form different from finding it in decimal form?

The main difference is that in fractional form, the area is represented as a fraction or ratio, while in decimal form, it is represented as a decimal number. This may be more useful when dealing with certain types of functions or when more precise calculations are needed.

What are the steps for finding the area below the graph of f in fractional form?

The steps for finding the area below the graph of f in fractional form are: 1) Divide the graph into smaller sections, 2) Calculate the area of each section using the formula for the area of a rectangle or triangle, 3) Add up all the individual areas to get the total area.

Can the area below the graph of f in fractional form be negative?

No, the area below the graph of f in fractional form cannot be negative. The area below the x-axis is considered negative, but when using fractions, this area is represented as a negative fraction, not a negative number. The total area will always be positive.

In what situations is finding the area below the graph of f in fractional form useful?

Finding the area below the graph of f in fractional form can be useful when dealing with functions that involve fractions, such as rational functions or trigonometric functions. It can also be helpful when more precise calculations are needed, as fractions can provide a more accurate representation of the area than decimals.

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