Use a double integral to find the area of R.R is the region bounded by y = 15x, y = ln x, y = 0, and y = 1.
A) $\int _ { y = 0 } ^ { y = 1 } \int _ { x = \frac { y } { 15 } } ^ { x = e ^ { y } } 1 d x d y = e - \frac { 31 } { 30 }$

B) $\int _ { y = 0 } ^ { y = 1 } \int _ { x = 0 } ^ { x =e ^ { y } } 1 d x d y = e - 1$

C) $\int _ { x= 0 } ^ { x - 2 } \int _ { y = \ln x } ^ { y =1 } 1 d y d x = e$

D) $\int _ { x = 0 } ^ { x= e } \int _ { y = \ln x } ^ { y = 15 x } 1 d y d x = \frac { 15 e ^ { 2 } } { 2 }$

Question

Use a double integral to find the area of R.R is the region bounded by y = 15x, y = ln x, y = 0, and y = 1.
A) $\int _ { y = 0 } ^ { y = 1 } \int _ { x = \frac { y } { 15 } } ^ { x = e ^ { y } } 1 d x d y = e - \frac { 31 } { 30 }$

B) $\int _ { y = 0 } ^ { y = 1 } \int _ { x = 0 } ^ { x =e ^ { y } } 1 d x d y = e - 1$

C) $\int _ { x= 0 } ^ { x - 2 } \int _ { y = \ln x } ^ { y =1 } 1 d y d x = e$

D) $\int _ { x = 0 } ^ { x= e } \int _ { y = \ln x } ^ { y = 15 x } 1 d y d x = \frac { 15 e ^ { 2 } } { 2 }$

Quizplus · Accepted Answer

The correct setup for the double integral to find the area of the region bounded by $y = 15x$, $y = \ln x$, $y = 0$, and $y = 1$ involves integrating with respect to $x$ first, from $x = \frac{y}{15}$ to $x = e^y$, and then with respect to $y$ from $y = 0$ to $y = 1$. This setup correctly accounts for the given boundaries and calculates the area of the region.

Use a Double Integral to Find the Area of R ∫y=0y=1∫x=y15x=ey1dxdy=e−3130\int _ { y = 0 } ^ { y = 1 } \int _ { x = \frac { y } { 15 } } ^ { x = e ^ { y } } 1 d x d y = e - \frac { 31 } { 30 }∫y=0y=1​∫x=15y​x=ey​1dxdy=e−3031​

Use a Double Integral to Find the Area of R $\int _ { y = 0 } ^ { y = 1 } \int _ { x = \frac { y } { 15 } } ^ { x = e ^ { y } } 1 d x d y = e - \frac { 31 } { 30 }$