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Integrate f Jov dV , wbere Q is the solid Ixnutuld by 0 :0. +2vplanes...

Question

Integrate f Jov dV , wbere Q is the solid Ixnutuld by 0 :0. +2vplanes

Integrate f Jov dV , wbere Q is the solid Ixnutuld by 0 :0. +2v planes



Answers

integrate $f$ over the given region. $\quad f(u, v)=v-\sqrt{u}$ over the triangular region cut from the first quadrant of the $u v$ -plane by the line $u+v=1$

Again in this question, we need to use just the region first. And now. Yeah, we have rice nicely. Thanks. Here. We don't have X y, but we have, uh you envy nobody. You hear, you hear? Okay. So I would be Can we use this very hand? You're not confusing with you. And now the first quantum's over here will be in the first quarter in Kenya on now we have to give us to be a question one. So it would be like this. You're being wonders and everyone said originally looking for me this one way Need Thio integrate different V minus square. It have been you other moderation here. So here we can send a the you devi and you goes from left to right. So it goes from there are to the lie on and you'II go do one minus v. So we're being one minus V and the TV will be from minimum valuable coaches. Are you no one? Now this the Brenda Corrie Goto would run the outer in the girl being me and inside we have, uh, integral arms. 0 to 1 minus v the man a skirt. You the u So we have this one that you want on because Visa Constant. So we should have the V. And now you and the limit from withdrawing to one minus V minus the new ICO Juba half. So we should have the u of 1/2 minus. One should be minus the way the fastest way to do with the integral of the and you About 1/2 that's gonna be you. About three on me. To be viable treatment, you will be Jew on the tree and I will have the limit from that. You want my honest me gave me. So we have included you go to one so we have him will be vey you. Put anything inside so we'll have the one minus B minus zero My nose. Uh, hey, we have ju I'm a tree, so have one minus v, uh, three on with you. And now we minus deserve to be about a mile Between what you Everything he had to do in the interview room. Don't leave me. So by certification we have in the government to one. And now we have here would be ah V minus V square my nose ju on with three one minus V about 32 Do you? So vision can be split into the tree in the garage from 0 to 1 brother to one from there to one. The 1st 1 with V D. V. The 2nd 1 with a V Square baby. And the last one would be well here we have minus with a constant cycle. Be Jewish 31 monastery about the tree with you, Do you be so doesn't be straight from what we should have here will be very square on with Ju and, uh, we were good together, so it would be much Vetri of ah three. We're not. Job done would be the limit from the 21 The last one. It requires our little bit more work here. What's there? We can do this one so we shouldn't have the integral I'm the one tree best you. So here's what you should be Bliss one. So it would be one minus B, just one. So we have five onward to and now divided. If I would use that we have here will be five times to hear So on now, because in some have one man this way so we have This one becomes a plus again. We have a new one, so it gives us a coach. You were the one inside with bundle. One of a Jew minus one of a three on glass Doesn't lose us. Echo Jew for off 15. And we wouldn't know one inside the gun is there also will be times there are on Dan minus far 15 again. Everybody is wrong. We've gotten one so many times. One on Doesn't he go to, ah, one with humans, One with threes and gives us Could you, uh, three months, two of Obama's over six minus for 1/5 day. So they go to one of the six minus far off day. You can leave dancer that this on. We can do one more step here. So the common denominator ego Judas. Uh, could you, uh, it's that they So it will be, Ah, that they, uh the 1st 1 times five No. So additional gives Amico. Jim. Ministry are days. You could you minus one. About 10

For F of X should be equal suit F of X. To be cool, too. two x and to evaluate the integra from There is one F of X. The eight is going to be equal to the integral from 30 to 1, two eggs, the eggs, and this will be two X squared Divided by two, the interval from 0 to 1. And this is X squared things ever from 0 to 1, and this would be equal to one squared. My name's zero squared, Which is equal to one.

Okay, so we're gonna integral dysfunction, X swim unless we're over Triangle Region Founded by 001001 I know that the three boundaries that's zero white zero and x plus y equals one. So let's call it Angel is I. And, uh, our exes from one is from 1 0 to 1 and our wise from 0 to 1 month. Ask us. Here we have X plus y x one in plus whites. Woman's ex. That's the reason. And our binge when integration is X squared plus y Elsewhere we have b y the eggs and we value this one first by integrated over Why? And we're gonna have 0 to 1 that's square miles. It's cute. Waas one of Jack's cute over three. And that part is in port the X. And finally, this is, um, excusable. Three months that's before before, minus one minus. As for Over fell from 0 to 1, which is was six

The given function is f of X, Come away as equals two X square Bless White Square on We have to integrate dysfunction over the triangular region. Whose works are is you don't coma. Zero one comma zero under zero comma one now first affordable Graph this What? This is on the graph paper to make a triangle region. So let's hear a graph paper now. So this is a graph paper on this. These have put the word This is zero comma 01 common zero. And this is zero comma one. And we had integrated the function over this region. No. So we can integrate. Isaac will still edible interrogate X squared plus y square Lord, do I d x, I'm taking the vertical strip. So the limits for Dubai here is why calls to zero on the equation of this line will be expressed. Why is equal to one from here? The value off why is the one minus six So it goes up to one minus x on for B X. That means for X limits are 0 to 1 zero. Now we have to simply indicate this Androgel or define so single and driven 0 to 1 on. I'll be integrating the in a book in a but first So I get X square. Why bless White Cube? Divide by three dot DX on the limits are from 0 to 1 minus six. Now are you? Plug in the limits, so get 0 to 1 x square. Why here is one minus six plus one minus X cubed whole cube Divide by three minus zero and plug zero. Here we get zero only. So not only to write, not be X No, we can simplify the inner function as 0 to 1 X squared minus six cube Bless one minus X to the power three. Divide by three daughter DX. Now we're going to integrate this function. So your ex cubed word by three My genetics to the bubble four. Divide before on Harry getting negative one minus X to the power off. Four. Divide by four times three's 12 on the limits are from 0 to 1. No, simply we have to plug the limits so we'll get one. Divide by three minus one. Divided by four. When I plug one hair, we get zeros on only two right minus the lower limit. When I plug zero Here we get 00 and hair. We get negative one by 12 so the skin Burjanadze I'll be combining these factions will get terrible times four ministries one bless one Divide by 12 which is equals to two. Divide by 12th. That is one divide. Wessex finally can conclude Dada in trigger 0 to 1 or the function X squared plus y square divide E X is equals to one divide by six.


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