# What is the average value of a function # y = x^2 (x^3 + 1)^(1/2) # on the interval #[0, 2]#?

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

To find the average value of a function ( y = x^2 \sqrt{x^3 + 1} ) on the interval ([0, 2]), you need to evaluate the definite integral of the function over that interval and then divide the result by the length of the interval.

First, compute the definite integral of the function ( y = x^2 \sqrt{x^3 + 1} ) over the interval ([0, 2]):

[ \int_{0}^{2} x^2 \sqrt{x^3 + 1} , dx ]

After finding this integral, divide the result by the length of the interval, which is (2 - 0 = 2). This will give you the average value of the function over the interval ([0, 2]).

Calculate the definite integral and then divide by 2 to find the average 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 find volume by rotating area enclosed by #y=x^3# and #y=sqrt(x)# about x=1?
- What is the general solution of the differential equation ? # 2xdy/dx = 10x^3y^5+y #
- What is the value of #F'(x)# if #F(x) = int_0^sinxsqrt(t)dt# ?
- How do you sketch the slope field for the differential equation #1/2 x +y -1#?
- #f:RR->RR;f(x)=e^x-x-1;g:[0,1]->RR;g(x)=f(x)+x#.How to calculate the volume of the body obtained by rotating the graph of the function "g" axis OX?

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