Which of the following definite–integral expressions gives the area of the region…

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

Problem

Which of the following definite–integral expressions gives the area of the region bounded by the curves

y=f(x)

and

y=g(x)

between

x=a

and

x=b

when the curves meet again at

x=c

(

a<c<b

) and satisfy

f(x)\ge g(x)

[a,c]

while

g(x)\ge f(x)

[c,b]

? (a)

\displaystyle \int_a^c [g(x)-f(x)]\,dx + \int_c^b [f(x)-g(x)]\,dx

(b)

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

(c)

\displaystyle \int_a^c [f(x)-g(x)]\,dx + \int_c^b [g(x)-f(x)]\,dx

(d)

\displaystyle \int_a^c [f(x)+g(x)]\,dx + \int_c^b [f(x)+g(x)]\,dx