For curves and with on the interval

MATHEMATICS · Single correct · AP · Calculus AB · Applications of Integration · Applications of Integration

Problem

For curves

y=f(x)

and

y=g(x)

with

f(x)\ge g(x)

on the interval

[a,b]

, which of the following integrals gives the area enclosed between the two curves from

x=a

x=b

? (a)

\displaystyle \int_a^b \bigl[f(x)+g(x)\bigr]\,dx

(b)

\displaystyle \frac12\int_a^b \bigl[f(x)-g(x)\bigr]\,dx

(c)

\displaystyle \int_a^b \bigl[f(x)-g(x)\bigr]\,dx

(d)

\displaystyle \int_a^b \bigl[g(x)-f(x)\bigr]\,dx