• Math10
When x is between -1 and 2 one of the functions is lower than the other. When you plot them can you see which it is? That is the lower bound. And the upper bound is the function that is higher.

## Homework Statement

Evaluate the double integral 4x^3 dA, where R is the region bounded by the graphs of y=(x-1)^2 and y= -x+3.

None.

## The Attempt at a Solution

The answer in the book is 72/5. But I got 45 as the answer.
Here's my work:
(x-1)^2= -x+3
x^2-2x+1= -x+3
x=2, -1
y=1, 4.
double integral of 4x^3 dx dy from -1 to 2 for dx and from 1 to 4 for dy
integral of x^4 (evaluate from -1 to 2) dy from 1 to 4 for dy
=45

Math10 said:

## Homework Statement

Evaluate the double integral 4x^3 dA, where R is the region bounded by the graphs of y=(x-1)^2 and y= -x+3.

None.

## The Attempt at a Solution

The answer in the book is 72/5. But I got 45 as the answer.
Here's my work:
(x-1)^2= -x+3
x^2-2x+1= -x+3
x=2, -1
y=1, 4.
double integral of 4x^3 dx dy from -1 to 2 for dx and from 1 to 4 for dy
No. The y values run from the parabola up to the line. They do not run from 1 to 4.
Math10 said:
integral of x^4 (evaluate from -1 to 2) dy from 1 to 4 for dy
=45

So how do I find the limits of integration for y?

Math10 said:
R is the region bounded by the graphs of y=(x-1)^2 and y= -x+3.
You get the limits from these equations. Did you draw a picture of this region?

Since it's a double integral, the x is from -1 to 2 for dx. What about y?

I still don't get it. What are the limits of integration for y?

When x is between -1 and 2 one of the functions is lower than the other. When you plot them can you see which it is? That is the lower bound. And the upper bound is the function that is higher.

The upper and lower bound varies with x. That's why you can't just use constants...you need to write the bounds in terms of functions. Try watching these 2 videos:

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Math10 said:
I still don't get it. What are the limits of integration for y?
I asked before, but you didn't respond. Did you sketch a graph of the region over which you're integrating?

You know what? I got it.