Let and for . Which of the following describes the value of ( _ -1 ^ 1 ! (f(x)-g(x) )…

MATHEMATICS · Single correct · A Level · Mathematics · Integration · Integration

Problem

Let

f(x)=x^{2}

and

g(x)=x^{2}+2

for

x\in[-1,1]

. Which of the following describes the value of

\displaystyle\int_{-1}^{1}\!\bigl(f(x)-g(x)\bigr)\,dx

? (a) It equals

4

because

g(x)-f(x)=2

on the entire interval. (b) It equals

0

because the integrand is even and the limits are symmetric. (c) It is negative because

f(x)-g(x)=-2

on the entire interval. (d) It is positive because both curves lie above the

x

–axis on the entire interval.