# What is the average value of the function # f(x)=e^(-x)*sin(x)# on the interval #[1, pi]#?

I get

Using the definition of a function's average value, we must determine

Lastly, divide the result by the interval's length to find the answer:

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

To find the average value of the function (f(x) = e^{-x} \cdot \sin(x)) on the interval ([1, \pi]), you can use the formula for the average value of a function over an interval:

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

where (a) and (b) are the endpoints of the interval.

In this case, (a = 1) and (b = \pi). So, we can plug these values into the formula:

[ \text{Average value} = \frac{1}{\pi - 1} \int_{1}^{\pi} e^{-x} \cdot \sin(x) , dx ]

Then, you would need to evaluate the integral to find the average value.

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

- How do you find the derivative using limits of #f(x)=2x^2+x-1#?
- How do you find the slope of the tangent line of #f(x) = 3-2x^3# at (-1, 5)?
- What is the equation of the line tangent to #f(x)=1/(1-3x)^2 # at #x=2#?
- What does differentiable mean for a function?
- What is the slope of the line normal to the tangent line of #f(x) = e^(x-3)/x+x^3 # at # x= 2 #?

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