# How do you find the average distance from the origin of a point on the parabola #y=x^2, 0<=x<=4# with respect to x?

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

To find the average distance from the origin of a point on the parabola ( y = x^2 ), ( 0 \leq x \leq 4 ) with respect to ( x ), you integrate the square root of the sum of squares of ( x ) and ( x^2 ) over the interval ( [0, 4] ), and then divide by the length of the interval ( 4 - 0 = 4 ). This can be expressed by the following formula:

[ \text{Average distance} = \frac{1}{4} \int_{0}^{4} \sqrt{x^2 + (x^2)^2} , dx ]

Solving this integral will give you the average distance from the origin.

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 find the volume bounded by #x^2y^2+16y^2=6# and the x & y axes, the line x=4 revolved about the x-axis?
- How do you find the general solution to #dy/dx+e^(x+y)=0#?
- What is the surface area of the solid created by revolving #f(x)=-2x^3-3x^2+6x-12# over #x in [2,3]# around the x-axis?
- How do you solve the differential #dy/dx=(x-4)/sqrt(x^2-8x+1)#?
- How do you use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region #y=1/x# and #2x+2y=5# rotated about the #y=1/2#?

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