# What is the average value of a function # f(t)= -2te^(-t^2)# on the interval #[0, 8]#?

The average value is

In this case we would have

If you want an approximation, use a calculator to get

Hopefully this helps!

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

To find the average value of the function ( f(t) = -2te^{-t^2} ) on the interval ([0, 8]), we use the formula for the average value of a function on a closed interval ([a, b]):

[ \text{Average value} = \frac{1}{b - a} \int_{a}^{b} f(t) , dt ]

For the given function ( f(t) = -2te^{-t^2} ) and the interval ([0, 8]), we have:

[ \text{Average value} = \frac{1}{8 - 0} \int_{0}^{8} (-2t)e^{-t^2} , dt ]

Now, we integrate ( f(t) ) from ( 0 ) to ( 8 ):

[ \int_{0}^{8} (-2t)e^{-t^2} , dt = \left[ -e^{-t^2} \right]_{0}^{8} = -e^{-64} + e^0 ]

So, the average value of ( f(t) ) on the interval ([0, 8]) is:

[ \frac{1}{8} \left( -e^{-64} + 1 \right) ]

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 differential #dy# of the function #y=2x-cot^2x#?
- How do you find the volume of the solid generated by revolving #y=10/x^2#, #y=0#, #x=1#, #x=5# about the y-axis?
- What is a second solution to the Differential Equation # x^2y'' -3xy'+5y=0 #?
- How do you find the volume of the solid bounded by #x=y^2# and the line #x=4# rotated about the x axis?
- What is a solution to the differential equation #dy/dx=2yx+yx^2#?

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