# How to integrate int ydx + zdy over a helix?

• i2837856393
In summary, the conversation is about solving a definite integral involving a helix equation with limits from 0 to pi. The resulting answer is 3(pi)/2 but the correct answer should be 3 pi. There may have been a typo in the problem or the teacher made a mistake.
i2837856393

## Homework Statement

$$\int$$ydx + zdy
C

where C is the part of the helix r(t)=(sin t)(i) + (cos t)(j) + t(k)
and 0 < t < pi (those should be greater than or equal to signs)

$$\int$$(cost)(cost)-t(sint)
$$\int$$(1+cos 2t)/2 - t sint
with limits from zero to pi.

this then equaled to
1/2t + (sin 2t)/4 + tcost -sin t

and this gave me the answer 3(pi)/2
but the answer should be 3 pi..
can anyone else solve this and check please or tell me where i went wrong.

I agree with your indefinite integral. But if i put the limits in I get -pi/2. That's still not 3*pi...? Is there a typo in the problem?

Last edited:
i'm sorry you're right...
that should be pi/2 - pi which is -pi/2
yea. then you and i are in agreement. i guess the teacher made a mistake. I've spent hours and this was the only solution i came to.

## 1. What is a helix?

A helix is a three-dimensional curve that is formed when a straight line is wrapped around a cylindrical surface at a constant angle and distance.

## 2. How do you represent a helix mathematically?

A helix can be represented mathematically using parametric equations, such as x = a cos(t), y = a sin(t), and z = bt, where a and b are constants and t is the parameter that determines the position along the helix.

## 3. What does it mean to integrate over a helix?

Integrating over a helix means finding the area under a specific function as it varies along the helix curve. This involves finding the limits of integration and using appropriate integration techniques.

## 4. How do you integrate int ydx + zdy over a helix?

To integrate int ydx + zdy over a helix, you first need to parameterize the curve using the parametric equations for a helix. Then, you can use the appropriate integration technique, such as line or surface integration, to find the area under the given function along the helix curve.

## 5. What are the applications of integrating over a helix?

Integrating over a helix can be useful in various fields such as physics, engineering, and mathematics. It can be used to find the center of mass of a helical object, calculate the work done by a force along a helix path, or determine the volume of a helical structure.

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