Determine, using the Simpson’s rule the area.Width (x)25811141720Height (y)-20232.10.1-2.2...

Determine the area enclosed by $$ \begin{array}{l} y=-\frac{1}{2} x-2 \\ y=\frac{1}{3} x-2 \\ y=0 \end{array} $$

Hello, everyone and welcome. So we want to use the area formula on the rectangle method. Essentially, um, to find the area under the curve for this function. And, of course, we're given this balance. So let's get started. So we know that the area is really just a summation. Ah, from this estimation from, um, icicle toe want to end off land times with so another way of writing that is essentially just f of so this right over here is the area formula, and then the rectangle method is what we're gonna do now. And we know this is therefore going to be equal toe when we factor out the six over end. Um, because remember, it's f it's ff six I over. And so, um, you have to apply this function up here. And now we have to distribute, um, this is equal to six or n. Yeah. So we're essentially just splitting up the submission, which allows us to tackle this a lot easier. No. Okay, so now that we have our expression, we can simplify it. So this is equal to, um And now we can just factor out some more, and, um, if you're wondering how we got this. It is just by evaluating summation, does this sort of the estimation properties? Um And so now we just have to really evaluate this expression and simplify it as we would anything else. And so what? We would end up getting here, Um, to some, algebra is negative. 18. So now we have this, and now we can set the limit as and of course, Infinity. So and so one thing to consider here and let's call this cause, jfx is that essentially we're gonna be making this term equal to zero. This time we go to zero, and this time we go to zero. And the reason is because when you divided constant by infinity, then we consider that equal to zero. So what, we really end up getting here is negative. Uh, after we get the limit. Actually, our answer to is really just gonna be negative 18 times too. Plus 72 because everything else has gone to zero, which is negative. 36 plus 72 which is 36 units square. Thank you for watching. And I hope this helped

Hey guys. So we know that the area of this rectangle is X to the power four plus 10 X squared plus 21 the length is extra post seven. So what would be the with of this rectangle right here? Well, then, with this just simply area divided by length. Right? Okay. Where kids actually power for? Plus 10 X square plus 21 divided by extra plus seven. Okay, so is there a way we can simplify this? Right. So let's start with the numerator. Let's try to do factoring for the numerator here. So if we let Xcor me you right well, we have then will have you square. Plus, can you please turn you one divided by U plus seven? Right? Okay, So the reason why I am letting I scored me you so that we can factor the numerator more easily right when we have only an expletive to Okay, so weekend factor The numerator by the sun product patterns. Totally fine. You guys do not remember what it iss. We're looking for two numbers whose some is 10 and whose product is one times 21. Okay. Can you guys think of any to such numbers. How about 37 till we worth? Right. So now we can break, tend you down into three. You and seven year, right? Just like that. All right, so for the first group, the common factor is useless. Factor you out. You scored about it by us. You plus three. You divided by us plus three. So similar to you. What? Which is dead. Now let's bring out the common factor, which is seven for groups and with you. And we'll also have you put three year. Okay, so now you plus three is our new Colin factory. Celeste, bring that out. Okay, So if you guys can see here, you plus seven is in both the top and the bottom of this fraction here. So we can totally that they let they cancel out and will only have you plus three here. So then you plus three is out with. And that is our final answer. Thank you so much for listening

Hi, guys. This problem is to approximate the area off the shadow of the region using the chaps Oi! The rule and Simpsons rule within the close to four so we can see if the function is denoted by fo X, then this shedded region has the area equal to integral from zero 24 fof ex the ex. So you ordered to use the Simpsons rule and chips ahoy the rule. We need to find the value off the function at 0123 and four. So from the graph, we can see f off zero You're close to three F off one equals two seven f offer to equals to NYU. F off three equals two seven and F 04 equals to zero. So bye, Chubbs. Oi! The rule the Negro From 0 to 4 f f x. The X is approximately equal to be minus a over to end. So it's the four minus zero over two times in and it's four says to 10 4 times fr zero, which is three plus two times f offer one which was seven plus two times, eh, For for two, which is nigh plus two times f off three, which is seven again and one times fo four, which is zero. So this number is equal to what half times three plus 14 plus 18 plus 14 again, and that is 24 0.5. So this is the approximation. Bye, Chubbs. Oi! The rule if we use The Simpsons rule than this into grow is approximately equal to four minus zero over three N times fr zero, which is three plus the four times F off one, which is seven plus two times off f off to which isn I plus four times F off three, which is seven again and then one times f off four, which is zero. So that is 1/3 times three plus 28 plus 18 plus 28 again, that is 77 over three, which is approximately equal to 25 0.67

The given question, We have to find the idea off the region. We can find it from the integration off effects, the X from zero to wait. So here the value off a street will you visit and the value of any signals to it. So the sub interval is one right. So with the help of trapezoidal method, we have relation. I hate ministry upon to into it after you know, plus 12 1 plus to have toe plus to have three class upto 12 7 plus have feet. We can read the values from the graph and we can subsidy substitute. We'll use We get jail plus two into one point. The plus 2 +123 doing to 5.7 going to get 0.9 plus two into them, plus two into nine, plus 26 plus trader. When the simplified is you get the result. As for 3.9 now we can find the with Delta Simpson method. So we have the exhibition for a definite in trickle. That is, the administrator appointed a into it after you know, plus four last one plus to have to plus four left Lee plus two of four plus upto F eight right so you can substitute the values from the Gulf. We get the final result as 44.6. So there yes, from the two method the episode and Simpson, a 43 point nine and 44.6 respectable.