You find the average of a set of numbers by adding them up and dividing by the number of terms. An integral is essentially a sum of all terms between and . So, you simply need to find the integral of the function, and divide it by the number of terms. In equation form:
f(averege)=1/(b-a)$f(x)dx...I'm using $ for the integral sign
a)1/3$[2,5](x^2-8x+16)dx
1/3[(x^3/3)-4x^2+16(evaluated from 2 to 5)
1/3[(5^3/3-4(5)^2-16(5))-(2^3/3-4(2)^2+16(2)]
1/3[(125/3-100-80)-(8/3-16+32)]
1/3[(125/3-180)-(8/3 +16)]
1/3(-415/3-56/3)
-471/9-ans