# Complex integration

• Calpalned
In summary, taking the derivative of both x and y with respect to t and then plugging it later gives the arc length of the parametric equation x = e^t + e^-t and y = 5 - 2t. This arc length is from 0 to 3. If this is the right integral, then how to compute it?f

## Homework Statement

The question involves finding the arc length of the parametric equation x = e^t + e^-t and y = 5 - 2t

## Homework Equations

Arc length of a parametric equation ∫√(dy/dt)^2 + (dx/dt)^2 dt limits are from 0<t<3

## The Attempt at a Solution

Taking the derivative of both x and y with respect to t and then plugging it later, I get
∫(2 + e^2t + e^-2t )^0.5 dt limits are from 0<t<3

Is this the right integral? If so, how do I compute it?

## Homework Statement

The question involves finding the arc length of the parametric equation x = e^t + e^-t and y = 5 - 2t

## Homework Equations

Arc length of a parametric equation ∫√(dy/dt)^2 + (dx/dt)^2 dt limits are from 0<t<3

## The Attempt at a Solution

Taking the derivative of both x and y with respect to t and then plugging it later, I get
∫(2 + e^2t + e^-2t )^0.5 dt limits are from 0<t<3

Is this the right integral? If so, how do I compute it?

Try to factor (2 + e^2t + e^-2t ) into a perfect square.

(2 + e^2t + e^-2t ) can be rewritten as e^2t(1) + 3^2t(e6^-4t) + 2(e^2t)(e^-2t) and by factoring
e^2t(1+e^-4t+2e^-2t)
Btw, how do I write equations in math form, because it's difficult type out exponents

(2 + e^2t + e^-2t ) can be rewritten as e^2t(1) + 3^2t(e6^-4t) + 2(e^2t)(e^-2t) and by factoring
e^2t(1+e^-4t+2e^-2t)
Btw, how do I write equations in math form, because it's difficult type out exponents
Look at the toolbar in the message box. It starts B I U ... and ends with ∑. Pressing the ∑ will give you access to Greek letters and other math symbols. Exponents and subscripts are accessed by pressing the x2 and x2 buttons on the toolbar.

(2 + e^2t + e^-2t ) can be rewritten as e^2t(1) + 3^2t(e6^-4t) + 2(e^2t)(e^-2t) and by factoring
e^2t(1+e^-4t+2e^-2t)
Btw, how do I write equations in math form, because it's difficult type out exponents

That's not the kind of factorization you need. You want to write it as (a+b)^2. Guess what a and b are.

I just solved it! The answer is e^3 - e^-3

Thank you so much