# Work Problem, Line Integral Fun (Calc 3)

• Weather Freak
In summary, a "Work Problem" in Calculus 3 refers to a type of problem that involves calculating the amount of work done by a force along a given path. This is usually done by taking the line integral of the force over the path. A line integral is used in "Work Problems" to calculate the work done by a force along a given path, taking into account the magnitude and direction of the force as well as the distance travelled. The main difference between a "Work Problem" and a traditional Calculus problem is that a "Work Problem" involves a physical application of calculus. To solve a "Work Problem" using line integrals, the given path must first be parameterized, then the unit tangent vector and force function
Weather Freak

## Homework Statement

Find the work done by the force field F(x,y) = x*sin(y) i-hat + y j-hat on a particle that moves along the parabola y = x^2 from (-1,1) to (2,4).

2. The attempt at a solution

The answer I get seems really, really, complicated and I have a hunch that it shouldn't be. Does anything look wrong in my work?

Thanks!

#### Attachments

• calc.jpg
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Hey,

The only thing I noticed is that your limits of integration seem to be off; t goes from -1 to 2, not -1 to 4. The integration is correct.

Awesome! Thanks :)

## What is a work problem in calculus?

A work problem in calculus involves calculating the amount of work done by a force acting on an object as it moves along a specified path. This is typically done by using the dot product of the force and the displacement of the object.

## How is line integral used in calculus?

Line integral is used in calculus to calculate the total value of a function along a specified curve or path. It involves breaking down the curve into small segments and approximating the function at each point to find the overall value.

## What is the difference between a line integral and a double integral?

A line integral is calculated along a single curve or path, while a double integral is calculated over a two-dimensional region. Line integrals are typically used for calculating work or finding the length of a curve, while double integrals are used to find volume or surface area.

## What are some real-world applications of line integrals?

Line integrals have many real-world applications, including calculating the work done by a force on an object, finding the mass of a wire with varying density, and analyzing the flow of a fluid through a pipe or channel.

## How can I improve my skills in solving work problem and line integral fun?

To improve your skills in solving work problems and line integrals, it is important to practice regularly and seek help from a math tutor or online resources when needed. It can also be helpful to review the fundamental concepts of calculus and familiarize yourself with different techniques for solving these types of problems.

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