# What is the arc length of #f(x) = x^2e^(3-x^2) # on #x in [ 2,3] #?

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

To find the arc length of the function ( f(x) = x^2 e^{3-x^2} ) on the interval ([2, 3]), we use the formula for arc length:

[ L = \int_{a}^{b} \sqrt{1 + [f'(x)]^2} , dx ]

First, find ( f'(x) ): [ f'(x) = 2xe^{3-x^2} - 2x^3e^{3-x^2} ]

Then, compute ( [f'(x)]^2 ): [ [f'(x)]^2 = (2xe^{3-x^2} - 2x^3e^{3-x^2})^2 ]

Now, integrate ( \sqrt{1 + [f'(x)]^2} ) from ( x = 2 ) to ( x = 3 ): [ L = \int_{2}^{3} \sqrt{1 + [f'(x)]^2} , dx ]

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

- What is a general solution to the differential equation #dy/dt+3ty=sint#?
- Solve # (1+x^2)^2y'' + 2x(1+x^2)y'+4y = 0 #?
- What is the arc length of #f(x)=xsinx-cos^2x # on #x in [0,pi]#?
- How do you find the carrying capacity of a population growing logistically?
- How do you calculate the arc length of the curve #y=x^2# from #x=0# to #x=4#?

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