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MATH1O93/MIS1OT1 Business MathematicsHomework: 3rd HW (Spring) Save Score: 0 of 2 pts 8 of 10 (2 complele) IW Score; 10%, 2 of 14.2.39 Queslion HelpEvaluatofl -3vr ...

Question

MATH1O93/MIS1OT1 Business MathematicsHomework: 3rd HW (Spring) Save Score: 0 of 2 pts 8 of 10 (2 complele) IW Score; 10%, 2 of 14.2.39 Queslion HelpEvaluatofl -3vr fl 3Vx +X dx =Enter VOur answer in Ihe answer box and Ihen click Check AnswerAll parts showingCiear AICiecAset

MATH1O93/MIS1OT1 Business Mathematics Homework: 3rd HW (Spring) Save Score: 0 of 2 pts 8 of 10 (2 complele) IW Score; 10%, 2 of 14.2.39 Queslion Help Evaluato fl -3vr fl 3Vx +X dx = Enter VOur answer in Ihe answer box and Ihen click Check Answer All parts showing Ciear AI CiecAset



Answers

Compute the definite integrals. Use a graphing utility to confirm your answers.

$$\int_{1}^{e} \ln \left(x^{2}\right) d x$$

Okay, so we have the girl of one over R one over each one of y'all and x x work with this solving their indefinite integral is pumping it in after. So what? Uh, what should we do if you continue to my heart's lets you all innovex do you is equal to one over x b x b that we have that Exelon of Ex smartest integral of just one X So we get that Exelon of minus X evaluated. That's one and one over. Eat. What is that? That's one A 11 minus one, minus one over E o N of one over E why it's one over. Eat that this simplifies to just get one too overt.

He's an integration by parts lights. Are you U to be equal to lane Oh, four plus X quake. That's great. So this implies that it's my BU. He's going to give me Sue X, divided by four plus eight squid. The X then gov he's going to be equal to the X, so this implies that fee is equal to words X. So now, Thank you Girl of Lane of four Plus six grade. The eggs is going to be equal to U V, which is X lane of four plus X quake. It's minus the integral of what's V D U, which is two eggs, four plus X squared. The X and this we can write it as in eggs. Laying off woods four plus X squared minus two outs is a constant, so we can bring that out in figure of we can express eggs divided by four plus Esqueda as one minus four, divided by four minus x quake The it's so using. So it means we can apply some rule here so that this will give us into X lean four plus X squared minus two. If I integrate this, what do I have? X then I integrate this part to get minus four. Divided by two Jackson Yeah, Eggs divided by two. Hey, say goodbye to let's see And this gives us yes, lane for less Ex quake minus two eggs. This is minus that. So that gives us plus four at them. Yes. Divided by two. Let's my way. See? So this thing implies that so this in place that's my instagram preserved to one of Len four. Let's X quake. The eggs is going to be equal to X like four plus X square, minus two eggs less four at a time at s divided by two which is going to we are evaluating from what, zero towards one. So this is going to give us Hey, Lane five. So life here because this is one one here so early in five minus two because they want, which is very good, which is so good to zone. So I have four at excess, one to act in one divided by two. And this is approximately one point 46 folks. That's fine Now results

Okay, so we have the integral of Joe, Degree of Poland, of X squared plus one. And the ex Cos integration reports looks find indifferent into the first. So we have you is equal to Ellen of Explorer one. The U S would do two x over a squared plus one. Then it's the TV is the X and B is equal to X to have exchanged Ellen of X squared plus one minus two. Interval of two X squared over X squared plus one ex. Okay, you can use Long Division on this if we do so, let's see. We have X squared and integral or divided by X squared, plus one to get one squared. So, like the one we have the major one. So we get one plus one over squared. We write that as extra one of X scored one minus two times in a row. All of one plus one over square one. The ex. You know that it's girl. That's actually so this is this sign. Invest. So nothing in this organ, we get X Ellen of exploited plus one minus two X minus 10 in burst of X. And now we need to evaluate this ad hoc. Reckon with Julia? No, it is three and I'm cracked being. So we get beat Three a one of 10 minus six minus to 10. Inverse of three. Minus your own morning. They're all working to invest. So to the simple vice, do you? Just 301 of 10.6 to 10 inverse of three.

In this question were to Seoul interrogation ex sex Squire two X dx and limited zero toe by by eight. Okay, so we have to solve it. So to solve this integral values integer integrate by parts on here you is equals two X that will give us do equals toe dx and D v is equals to sex square two x dx Then we will be 10 2 x divided by two. Okay. And now we will use the formula interrogation off you d v will be you dot We minus indication off video. Okay, If it is in limit areas, Toby, then it will be a tow me. Okay, now you is X and V is 10 two x by two okay. And minus Interrogation off V is 10 two x by two on Do you is dx hair okay. And it will be under zero to pi by eight. Okay. And it can be further written as x. Yeah, that is x 10 2 x by two and it will be minus one by two out of the integration and it will be 10 2 x dx and it will be zero to buy by eight. Okay, Now we know. What is the indication off then? X, That is way. Just write the formula. Hair. It will be interrogation off. Then you you will be one by minus one by coefficient off you and Ellen cause you Okay, so it will be like x 10 2 X by two minus one by two. And it will be It will be won by two. Ellen caused two X. Okay, So simple. And it will under 02 by by eight. Now it will be x 10 2 x divided by two on my it is minus. So it will be minus minus. Plus one by four. Ellen cost two x on in 0 to 58 Okay. Now again, it will be. Now we will put the values off limits hair so fast by by eight and then zero and it will be passed by by eight. Then it will be by by 16 and tend to X. That is 10. Bye bye. Four. Okay, that is one. Okay. And plus one by four. Ln caused to buy. That is caused 45. Okay, of course. Two into pi by it. That inspired by four. Okay, on. When we put zero, Then it will be zero plus Ellen. One that is also zero. Then it is zero. Okay, so there are four bars. 123 and four. So all the values it first will be by by 16. And second will be won by four. Ln on it will be won by Roto. Okay. And 3rd and 4th will be zero. And when we saw it, will gives us answer. Approximate to 0.1097 Okay. And that will be our final. I'm sad. Thank you.


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