Average Value Question

Question

What is the average value of the function f(x)=xe^{x^2} on the interval [1,3]?

a.1/4(e³-e)

b.1/4(e⁹-e)

c.1/2(e⁹-e)

d.1/2e⁹

e. e⁹-e

f. None of the above

Answer 1

Average value of y = f(x) from x = a to x = b is (1/(b-a))∫_{from a to b} f(x)dx

So, we have (1/(3-1))∫_{(from 1 to 3)} xe^{x^2}dx

= (1/2)[(1/2)e^{x^2}]_{from1 to 3} = (1/4)(e⁹ - e)