# What is the arclength of #(t^2lnt,lnt^2)# on #t in [1,2]#?

Performed by WolframAlpha

Let L be the parametric arclength, then the formula is:

Substitute the above into the formula:

Integration performed by WolframAlpha

By signing up, you agree to our Terms of Service and Privacy Policy

To find the arc length of the curve defined by the parametric equations (t^2ln(t), ln(t^2)) for t in the interval [1, 2], we use the formula for arc length:

L = ∫[a,b] √[ (dx/dt)^2 + (dy/dt)^2 ] dt

Substituting the parametric equations into the formula, we have:

L = ∫[1,2] √[ (d/dt(t^2ln(t)))^2 + (d/dt(ln(t^2)))^2 ] dt

After taking the derivatives and simplifying, we get:

L = ∫[1,2] √[ (2tln(t) + t)^2 + (2/t)^2 ] dt

Now, we integrate this expression over the interval [1,2] to find the arc length. This integral might not have a closed-form solution, so numerical methods or software may be used to approximate the value.

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- How do you differentiate the following parametric equation: # x(t)=cost, y(t)=sint #?
- How do you write #x = e^t-1# and #y=e^2t# as a cartesian equation and then sketch the curve?
- How do you differentiate the following parametric equation: # x(t)=(1-t)/e^t , y(t)=t/e^(3t) #?
- What is the derivative of #f(t) = (t^2+1 , e^(-t^2-t) ) #?
- How do you change the parametric equation to cartesian equation #x = t^2 - 1# and #y = t^3#?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7