# calculus

Calculate he average over the given interval: f(x)=e^(-n*x), [-1,1].

I know that the average value = (1/b-a)integrate from a to b f(x)dx

1. 👍
2. 👎
3. 👁
1. You have stated the definition of the average value correctly. All you have to do is perform the integration and divide the integral by the integration interval, 2.

The indefinite integral of e^(-nx) is (-1/n)*e^(-nx).

The definite integral from -1 to 1 is
(-1/n)[e^-n - e^n]

Divide that by 2 for the average value.

Check my math. I am often sloppy.

1. 👍
2. 👎
2. thanks, but can we leave it in that form?

1. 👍
2. 👎
3. You can convert my answer to a hyperbolic sine of n, divided by 2, if you wish.

1. 👍
2. 👎
4. I meant "divided by n", not 2

1. 👍
2. 👎
5. What is hyperbolic sin of n? Never heard of that.

1. 👍
2. 👎

## Similar Questions

1. ### mathematics

Use the table to calculate the average rate of change of f(x) over the interval [0,4]. x f(x) -4 1 -3 2 -2 4 -1 8 0 16 1 32 2 64 3 128 4 256

2. ### science

A ball rolling down an incline travels 6.0 cm in the first 0.25 econds, and 24 cm in the first 0.50 seconds. Find: a)The average speed for the first quarter second time interval B) The average speed for the second time interval C)

3. ### Physics

Two motorcycles are traveling due east with different velocities. However, four seconds later, they have the same velocity. During this four-second interval, cycle A has an average acceleration of 1.8 m/s2 due east, while cycle B

4. ### AP CALC

1. Let f be a twice-differentiable function such that f (2) = 8 and f (4) = 5. Which of the following must be true for the function f on the interval 2 ≤ x ≤ 4. I. The average value of f is 6.5 II. The average rate of change

1. ### physics

the earth is,on average,150 million km from the sun.calculate its average speed in orbit.

2. ### Mathematics

Examine the following graph of the linear function f(x)=2x+1 and the quadratic function g(x)=−116(x+3)2+6. Graph of g of x is a downward opening parabola that passes through points (negative 4, 5), (negative 3, 6), & (1, 5). f

3. ### Physics

At an air show, a jet plane has velocity components vx = 695 km/h and vy = 440 km/h at time 4.85s and vx= 933km/h and vy = 465 km/h at time 7.12 s. For this time interval, find (a) the x and y components of the plane’s average

4. ### Rate of Change from a Table Quick Check

Here are the answers for the Connexus Rate of Change from a Table Quick Check. Q1. The following table represents the altitude of a hiker climbing a mountain over a 60-minute hike. Calculate the average rate of change over the

1. ### calculus

The Average value of f(x)=25−x^2 on the interval [0,1] is 74/3 Find a value c in the interval [0,1] such that f(c) is equal to the average value?