# How do you find the average value of the function #u(x) = 10xsin(x^2)# on the interval #[ 0, sqrtpi ]#?

The average value is

The average value requested in the question is:

An alternative query

The topic "Average Rate of Change..." is where the question was posted, and it differs from the average value.

Throughout this period, this function's average rate of change is

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

To find the average value of the function ( u(x) = 10x\sin(x^2) ) on the interval ([0, \sqrt{\pi}]), you need to compute the definite integral of the function over the given interval and then divide the result by the length of the interval.

- Compute the definite integral of ( u(x) ) over the interval ([0, \sqrt{\pi}]) using the Fundamental Theorem of Calculus.
- Find the length of the interval, which is ( \sqrt{\pi} - 0 = \sqrt{\pi} ).
- Divide the result from step 1 by the length of the interval found in step 2.

[ \text{Average value} = \frac{1}{\sqrt{\pi}} \int_{0}^{\sqrt{\pi}} 10x\sin(x^2) ,dx ]

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 average rate of change for the function #f(x) = 2 / (x+1)# on the indicated intervals [0,h]?
- How do you find the equation of a line tangent to the function #y=sqrtx+1# at x=4?
- What is the equation of the line normal to #f(x)= xsin^2(2x) # at #x=pi/8#?
- What is the equation of the tangent line of #f(x) =(e^3x-3x)(e^x-x)# at #x=1#?
- How do you determine at which the graph of the function #y=x^4-8x^2+2# has a horizontal tangent line?

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