Let for , where is a real constant. The average value of on the closed interval is…

MATHEMATICS · Subjective · AP · Calculus AB · Applications of Integration · Applications of Integration

Problem

Let

f(x)=kx^{2}+3x

for

0\le x\le 4

, where

k

is a real constant. The average value of

f

on the closed interval

[0,4]

is required to be

10

. Determine the value of

k

that satisfies this condition. Show all steps in your reasoning.