Let be defined on the interval

MATHEMATICS · Multi-part · AP · Calculus AB · Applications of Integration · Applications of Integration

Problem

Let

g(x)=kx^{2}

be defined on the interval

[0,3]

. It is known that the average value of

g

over this interval equals

6

. (i) Write the mathematical expression representing the average value of

g

[0,3]

. (ii) Compute the value of the constant

k

that satisfies the given condition.