## Related questions with answers

Question

Write the limits for the double integral

$\int_R \int f(x, y) d A$

for both orders of integration. Compute the area of $R$ by letting $f(x, y)=1$ and integrating.

Triangle: vertices $(0,0),(3,0),(2,2)$

Solution

VerifiedAnswered 2 years ago

Answered 2 years ago

Step 1

1 of 6$\int_{0}^{2}\int_{0}^{x}dydx+\int_{2}^{3}\int_{0}^{-2x+6}dydx=\int_{0}^{2}\int_{y}^{-.5y+3}dxdy$

To integrate in the order of $dydx$, the triangle must be broken up into 2 parts. Chop the triangle using $x=2$. The boundaries of the first triangle are $y=x, y=0, x=2$. To find out the upper $y$ limit in the second integral, find the equation of the line between (2,2) and (3,0). The boundaries of the second triangle are $y=-2x+6, y=0, x=2$. To integrate in the order of $dxdy$, you need to solve for $x$ in $y=x, y=-2x+6$.

## Create a free account to view solutions

By signing up, you accept Quizlet's Terms of Service and Privacy Policy

## Create a free account to view solutions

By signing up, you accept Quizlet's Terms of Service and Privacy Policy

## Recommended textbook solutions

#### Thomas' Calculus

14th Edition•ISBN: 9780134438986 (11 more)Christopher E Heil, Joel R. Hass, Maurice D. Weir10,142 solutions

#### Calculus: Early Transcendentals

8th Edition•ISBN: 9781285741550 (4 more)James Stewart11,085 solutions

#### Calculus: Early Transcendentals

9th Edition•ISBN: 9781337613927 (1 more)Daniel K. Clegg, James Stewart, Saleem Watson11,049 solutions

## More related questions

1/4

1/7