A Level

MATHEMATICS · Multi-part · A Level · Mathematics · Integration · Integration

Problem

Let

f(x)=3x^{2}-6x+4

for

1\le x\le 4

. (a) Find an antiderivative

F(x)

f(x)

that satisfies

F(0)=0

. (b) Calculate the exact value of

\displaystyle \int_{1}^{4} f(x)\,dx

. (c) Interpret the result from part (b) as a geometric quantity. Include appropriate units in your statement.