Mathematics

Problem

Let the region R be bounded on the right by the curve

x = g_1(y)

, on the left by the curve

x = g_2(y)

, and vertically between

y=c

and

y=d

, where

g_1(y)\ge g_2(y)

for all

y

[c,d]

. Which of the following definite integrals gives the area of R? a)

\displaystyle\tfrac12\int_{c}^{d} \bigl[g_1(y)+g_2(y)\bigr]\,dy

\displaystyle\int_{c}^{d} \bigl[g_2(y)-g_1(y)\bigr]\,dy

\displaystyle\int_{c}^{d} \bigl[g_1(y)-g_2(y)\bigr]\,dy

\displaystyle\int_{g_2(c)}^{g_1(d)} (d-c)\,dx