What is the Solution to a Challenging Integration Homework Problem?

In summary, a student asked for help with a problem involving drawing a graph and finding the integral of a function. The person responding advised the student to draw a picture and consider the points (5, 13) and (11, 6) to sketch a possible graph. They also suggested drawing the boundaries of the region for the given integral and then comparing it to the region for the integral of the inverse of the function.
  • #1
MillerL7
14
0
I attached just one question...My tutor and the TA could not figure it out or help me get started on it...can someone help me get started? Thank you so much!
 

Attachments

  • Integration One.doc
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  • #2
First Please type the problem in rather that posting a "word" file. It's not that difficult and many people won't open a "word" attachement for fear of viruses. I wouldn't if I didn't have very strong virus protection.

As for the problem itself, Draw a picture. While you don't know the exact "form" of f, you know that it passes through the points (5, 13) and (11, 6) and is decreasing so you can sketch a possible graph for f. You also know that the integral given is the area under that curve- the area between that curve and the x-axis. Draw the boundaries of that region.

Now, f-1 just "swaps" x and y so the integral of f-1 you are looking for is the area between that curve and the y- axis. Draw the boundaries and conpare the two areas.
 

Related to What is the Solution to a Challenging Integration Homework Problem?

What is integration homework problem?

Integration homework problem refers to a type of mathematical exercise that involves finding the antiderivative or integral of a given function. It is a fundamental concept in calculus and is used to solve a variety of real-world problems.

How do I solve an integration homework problem?

To solve an integration homework problem, you must first identify the function and the limits of integration. Then, you can use integration techniques such as substitution, integration by parts, or partial fractions to find the antiderivative. Finally, evaluate the antiderivative at the given limits to obtain the solution.

What are the different types of integration techniques?

There are several integration techniques, including substitution, integration by parts, partial fractions, trigonometric substitution, and integration by trigonometric identities. Each technique is used to solve different types of integration problems and can be applied depending on the complexity of the function.

Why is integration important in science?

Integration is essential in science because it allows us to model and understand the behavior of complex systems. It is used in various fields of science, such as physics, chemistry, and biology, to analyze and solve problems related to motion, growth, and change.

What are some common mistakes to avoid when solving integration homework problems?

Some common mistakes to avoid when solving integration homework problems include forgetting to add the constant of integration, incorrectly applying integration rules, and making algebraic errors. It is also essential to check your solution by differentiating it to ensure that it matches the original function.

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