Using Green's Theorem, calculate the area of the indicated region.
-The area bounded above by $y = 3 x$ and below by $y = 10 x ^ { 2 }$
A) $\frac { 9 } { 80 }$
B) $\frac { 9 } { 200 }$
C) $\frac { 3 } { 200 }$
D) $\frac { 9 } { 100 }$

Question

Quizplus · Accepted Answer

Green's Theorem relates a line integral around a simple closed curve to a double integral over the plane region bounded by the curve. The area can be found using the formula $\frac{1}{2} \oint_C (x \, dy - y \, dx)$. For the given curves, the intersection points are $x = 0$ and $x = \frac{3}{10}$. Calculating the integral gives the area as $\frac{9}{200}$.

Using Green's Theorem, Calculate the Area of the Indicated Region y=3xy = 3 xy=3x

Using Green's Theorem, Calculate the Area of the Indicated Region $y = 3 x$