# What is the arclength of #f(t) = (t^3-t^2+5t,9t)# on #t in [1,4]#?

Use

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

To find the arc length of ( f(t) = (t^3 - t^2 + 5t, 9t) ) on ( t ) in the interval ([1,4]), we first need to compute the derivative of ( f(t) ), then integrate the square root of the sum of the squares of the derivatives over the given interval. The arc length formula is given by:

[ \int_{a}^{b} \sqrt{\left(\frac{dx}{dt}\right)^2 + \left(\frac{dy}{dt}\right)^2} dt ]

Substituting the derivatives of ( f(t) ) into the formula and evaluating the integral over the interval ([1,4]) will give us the arc length.

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.

- What is the derivative of #f(t) = (t-lnt^2, t^2-sint ) #?
- What is the derivative of #f(t) = (t^2-sint , t-e^t ) #?
- What does the graph #r = sqrt(sintheta)# look like in plane polar coordinates? How do you graph it?
- How do you differentiate the following parametric equation: # x(t)=-te^t+t, y(t)= 3t^2+2t #?
- What is the significance of partial derivative? Give an example and help me to understand in brief.

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