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Question (4 points ): The double integral J6 f35xy2 dxdy has rectangular region.Select one:TrueFalse...

Question

Question (4 points ): The double integral J6 f35xy2 dxdy has rectangular region.Select one:TrueFalse

Question (4 points ): The double integral J6 f35xy2 dxdy has rectangular region. Select one: True False



Answers

Determine whether the statement is true or false. Explain your answer. If $R$ is the region in the $x y$ -plane enclosed by $y=x^{2}$ and $y=1$, then $$ \iint_{R} f(x, y) d A=2 \int_{0}^{1} \int_{x^{2}}^{1} f(x, y) d y d x $$

So let's start by force to fall visualizing this region So we have. Why is equal to squared off X And here's the line wise equal to two and we wanna rotate this about the y axis. So for the elemental desk, the radius our people to X and the thickness is equal to divide. So we can say that the elemental volume D Y is equal to pi r squared divide or pi times x squared d y. And since we have, why is equal to square it off extract gives me X is equal to y squared, which gives me X squared is equal to y to the power for so the volume were people to any girl from 0 to 2 high times y to the power for delight and that means that given statement is false.

In this problem we will cover double integrates with polar coordinates. So if we wanted to turn the integral on our left in blue are you are right but to the left of the equal sign into a double integral with polar coordinates. There are a couple of things that we have to do. First, we know that D. A. Is going to be rewritten as our D. R. D. Data. Second we know that the inside function X plus Y is going to be rewritten as our coast data plus our sign data. And we want to find our bounds. So we know that our bounds for the integral pertaining to our are going to be From 0 to 3 because our region are to the left is a semicircle and the first two quadrants of the graph And it has a radius of three. And we know that the bounds for our integral pertaining to the angle data are going to be from zero. It's a pie because like I said we have a semicircle and those are just in the first two quadrants. So with all of us together uh we can create our devil integral. So are outside integral will be zero. High are inside integral would be 0 to 3. We have our polar function, our coast data plus our sign data which I guess we can simplify or just rewrite. We can pull out our from both. So we have our Costa was signed data times are D. R. D. Theta. And this can be simplified. Once again we can multiply the two ours together. And so instead of having this art here, we just have R squared D r D. Theta. So this should be our actual double integral and not the one here. That means the statement given is false.

The question. They're predicting my mother. This statement is four. The statement is the area of the region. Off in ex lightly is given by double figures. Were the region on the fly, the no movement towards the solution, the eminent statement, this fall's and the correct statement for the media off the original? It's normal in regulation or one of the regional D, and this is the final answer for a given question and you?

In the question they regret remain. Whether that statement given a statement, it's supposed that some region in the and slightly is a really big or the regional open ex wife is zero if honest, something like a movie just like a and R devil. Integration over the region are one off events. Why the is a off the bill? Indignation off over the region are affects by the now moving towards dissolution. The given indigenous integration over the region are if it's like the which is zero. So as history is divided into four parts that are so we can return as devil, integration over the region are less off FX. Why? The is a specific that is double integration. Over the region are one FX white. The less double invigoration over the effects, like the physicals to zero. So it will make double invigoration of delusion are what effects Why the negative and fix light the hence that Afghanistan is and and this is the final Lots of ridiculous question. Thank you


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