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Your Type II Integral

mark

(10 pts)

In this problem, you’re going to use Desmos to help you set up a tricky Type II integral. To get the exact statement of your problem, choose your name from the following list:

audrey

My region is stuck between the curves

x = 2 y^4-8 y^3-8 y^2+2 y-6

and

x = -5 y^4+9 y^3+4 y^2-6 y+9.

Demos says that looks like so:

Reading from the graph, I can see that my area could be expressed as the following iterated integral:

\int_{-1.176}^{2.96} \int_{2 y^4-8 y^3-8 y^2+2 y-6}^{-5 y^4+9 y^3+4 y^2-6 y+9} 1 \, dx \,dy.

rstahles

My type II region is stuck between the curves:

x = 4 y^4-7 y^3-10 y^2+5 y-10

and

x = -6 y^4+6 y^3+2 y^2-6 y+6

Using Desmos, I graphed my curves to illustrate my region:

Reading from the graph, I can see that my area could be expressed as the following iterated integral:

\int_{-1.236}^{1.871} \int_{4 y^4-7 y^3-10 y^2+5 y-10}^{-6 y^4+6 y^3+2 y^2-6 y+6} 1 \, dx \,dy.

ScottLashley

The type II region stuck between the curves that I was given is
x = 7 y^4-11 y^3-6 y^2+3 y-6 and x = -6 y^4+7 y^3+2 y^2-6 y+8
Here is my graph:

My area can be expressed as the following iterated integral:
\int_{-1}^{1.72} \int_{7y^{4}-11y^{3}-6y^{2}+3y-6}^{-6y^{4}+7y^{3}+2y^{2}-6y+8} 1 \, dx \,dy

whardin3

My region is stuck between the curves,

x= (11y^4)-(5y^3)-(11y^2)+2y-7
and
x=(-4y^4)+(8y^3)+(8y^2)-6y+3
Desmos shows that this is where the region lies.

From the graph, my area can be expressed using the following iterated integral:
\int_{-1.131}^{1.608} \int_{11y^4-5y^3=11y^2y-7}^{-4y^4+8y^3+8y^2-6y+3} 1dxdy.

Colby_Howell

My region lies between the curves

x=6y^4-2y^3-6y^2+6y-11

and

x= -7y^4+4y^3+8y^2-11y+12

With desmos, I got a graph that looks like this:

When looking at the graph, I find that my area could be expressed by this iterated integral

\int_{-1.459}^{1.309}\int_{6y^4-2y^3-6y^2+6y-11}^{-7y^4+4y^3+8y^2-11y+12}1dA

fcarrill

My region is stuck between the curves
7y^{4}-5y^{3}-4y^{2}+6y-8
and
-12y^{4}+2y^{3}+3y^{2}-2y+11
Demos says that looks like so:

Reading from the graph, I can see that my area could be expressed as the following iterated integral:
\int_{1.102}^{-1.092} \int_{7y^{4}-5y^{3}-4y^{2}+6y-8}^{-12y^{4}+2y^{3}+3y^{2}-2y+11} 1 \, dx \,dy.

impish_wyvern

My region is between the curves x = 6 y^4-5 y^3-7 y^2+10 y-9 and x = -11 y^4+2 y^3+5 y^2-8 y+6

My Desmos plot shows it as such:
Therefore, my given area as expressed by an iterated integral would be:

\int_{-1.259}^{0.975}\int_{ -11 y^4+2 y^3+5 y^2-8 y+6}^{6 y^4-5 y^3-7 y^2+10 y-9}1dx dy.

myost

my region is stuck between the curves

x=6y^2-12y^3-12y^2+8y-10

and

-2y^4+3y^3+3y^2-6y+2

Desmos says that looks like:

From the graph, I can see that the area can be expressed as:

\int _{-1.2973}^{2.4506} \int_{6y^4-12y^3-12y^2+8y-10}^{-2y^4+3y^3+3y^3-6y+2} 1 \, dx \,dy.

mearing

My region is stuck between the curves:

x=7y^4-2y^3-10y^2+4y-10

and

x=-8y^4+11y^3+9y^2-7y+6

My desmos plot looks like this:

My area can be expressed with the following iterated integral:

\int_{-1.228}^{1.62}\int_{7y^4-2y^3-10y^2+4y-10}^{-8y^4+11y^3+9y^2-7y+6}1\space dx \space dy

Alexander_The_OK

x=4y^2-3y^3+12y-12)

x=-9y^4+6y^3$+4y^2-12y+10

the area inside the two curves is the integral. The x points are 16.236 and -18.469, so we get the integral

\int_{-18.469 }^{16/236}\int_{-9y^4+6y^3$+4y^2-12y+10}^{4y^2-3y^3+12y-12}1dxdy

knguyen3

My region is enclosed by the curves:
x=11y^4-11y^3-10y^2+2y-4
and
x=-9y^4+7y^3+9y^2-6y+2
Below is the graph:

The iterated integral of the enclosed region in the graph is:

\int_{-0.936}^{1.46}\int_{11y^4-11y^3-10y^2+2y-4}^{-9y^4+7y^3+9y^2-6y+2}1dxdy

jlajcin

My type II region is in between the curves:

x= 4y^4-12y^3-6y^2+3y-3

and

x=-6y^4+10y^3+4y^2-5y+9

Desmos graphs it as such:

Reading the graph, you can see the area can be expressed as the following iterated integral:

\int_{-.973}^{2.543} \int_{4y^4-12 y^3-6 y^2+3 y-3}^{-6 y^4+10 y^3+4 y^2-5 y+9} 1 \, dx \,dy.

sophiem

My region is between the curves
x = 2 y^4-9 y^3-10 y^2+5 y-9
and
x = -3 y^4+7 y^3+11 y^2-2 y+3.

Here is the graph:

The area can be expressed with the integral
\int_{-1.398}^{4.162} \int_{2 y^4-9 y^3-10 y^2+5 y-9}^{-3 y^4+7 y^3+11 y^2-2 y+3} 1 \, dx \,dy.

aaudia

My region is stuck between the curves

x = 6y^4-12y^3-12y^2+3y-11

and

x = -3y^4+12y^3+9y^2-7y+3.

I’ve embedded the Desmos graph below.

The area between the curves can be expressed as the following iterated integral:

\int_{-1.161}^{3.313} \int_{6 y^4-12 y^3-12 y^2+3 y-11}^{-3 y^4+12 y^3+9 y^2-7 y+3} 1 \, dx \,dy.

jsublett

My type II region is stuck between the curves:

x=7y^4 - 11y^3 - 6y^2 + 9y - 6

and

x = -11y^4 + 12y^3 + 10y^2 - 2y +9

Using Desmos, I graphed my curves to illustrate my region:

Reading from the graph, I can see that my area could be expressed as the following iterated integral:

\int_{-1.01}^{1.744} \int_{7y^4 - 11y^3 - 6y^2 + 9y - 6}^{-11y^4 + 12y^3 + 10y^2 - 2y + 9} 1 dx dy

mhernan5

My type II region is stuck between the curves:
x=3y^4-10y^3-12y^2+11y-7
and
x=-9y^4+10y^3+2y^2-3y+7
Using Desmos, I graphed the curves to illustrate my region:

My area can be expressed as the following iterated integral:
\int_{-1.123}^{2.086}\int_{3y^{4}-10y^{3}-12y^{2}+11y-7}^{-9y^{4}+10y^{3}+2y^{2}-3y+7}1\ dx\ dy

mbanawan

My region is between the curves

x = 11y^4 - 10y^3 - 3y^2 + 8y - 7

and

x = -9y^4 + 9y^3 + 9y^2 - 11y + 7

My region in desmos looks like:

jbrenema

My region is between the curves:

x=9y^4-6y^3-2y^2+11y-11

and

x=-11y^4+7y^3+3y^2-3y+10

And according to Desmos, looks like this:

My graph can be expressed as the following iterated integral:

\int_{-1.066}^{1.095} \int_{9 y^4-6y^3-2y^2+11y-11}^{-11 y^4+ 7y^3+ 3y^2- 3y+10} 1 \, dx \,dy.

mparog

The Region stuck between the curves given:

x = 10y^4 - 5y^3 - 5y^2 + 9y - 6

x = -11y^4 + 6y^3 + 4y^2 - 5y + 9

Here is the Graph:

The Area can be expressed as:

\int_{-1.063}^{1} \int_{10y^4 - 5y^3 - 5y^2 + 9y - 6}^{-11y^4 + 6y^3 + 4y^2 - 5y + 9} 1 dx dy