# Sketching Region of Integration of unspecified function?

## Homework Statement

Double integral (The first one is lower bound 0 and upper bound 1, the second one is lower bound 7x and top one 7). of f(x,y)dydx and my teacher wants me to sketch the region of integration. Then reverse the area of integration.

## The Attempt at a Solution

So I was thinking about this and trying to figure out how to do this with an unspecified function.. Could I just show in random functions like (xy) or (x^2)(y^2) and look for some sort of pattern? Am I on the right track here as far as the methodology of solving the problem goes?

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Mark44
Mentor

## Homework Statement

Double integral (The first one is lower bound 0 and upper bound 1, the second one is lower bound 7x and top one 7). of f(x,y)dydx and my teacher wants me to sketch the region of integration. Then reverse the area of integration.

## The Attempt at a Solution

So I was thinking about this and trying to figure out how to do this with an unspecified function.. Could I just show in random functions like (xy) or (x^2)(y^2) and look for some sort of pattern? Am I on the right track here as far as the methodology of solving the problem goes?
No, you're not on the right track. The function in the integrand doesn't matter.

Here's your integral, laid out in LaTeX:
$$\int_{x = 0}^1 \int_{y = 7x}^7 f(x, y) dy~dx$$

The inner integral is with x held fixed and y varying; the outer integral is with x varying.

LCKurtz
Homework Helper
Gold Member
And the way to do a problem like this is to sketch the region, as your teacher requested. Once you have the region sketched, set the integral up as a dxdy integral using the sketch. So what does your sketch look like and what did you get when you reversed the limits?

HallsofIvy
$$\int_{x=0}^1\int_{y= 7x}^7 f(x,y)dydx$$