The quadratic function is defined for .

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

Problem

The quadratic function

f(x)=3x^{2}+4x

is defined for

1\le x\le 4

. (i) Calculate the area enclosed between the graph of

y=f(x)

, the

x

-axis, and the lines

x=1

and

x=4

. (ii) Using your answer to part (i), determine the average (mean) value of

f(x)

on the interval

[1,4]

. Express your answer as an exact fraction.