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Example 9.1graph of f(c) Tct/4 +4 on [0,3]. Determine the area under theTct/...

Question

Example 9.1graph of f(c) Tct/4 +4 on [0,3]. Determine the area under theTct/

Example 9.1 graph of f(c) Tct/4 +4 on [0,3]. Determine the area under the Tct/



Answers

Determine the total area between the curve and the $x$ -axis shown in Fig. Ex. 31.

Discussion we able to find the area of the region under the car up and uh, what do you have to use is fXc crystal XQ Plastics. And the limits within the 0-1 year. To find the idea. So to calculate the area bounded by the car, you have to integrate the function. Okay. Within the given limits We didn't have given him 110-1. No, I replace the value of function that is execute less sex. And we all know that integration of excuses next to the power for divide by four. An integration of access access square by two. Okay. No, the they place here the limits. Initially we put to Parliament that dividends you won by four plus one by two. And if you put zero then both the terms changes in 2:00. He had a good take. They'll see him four and then he should get three by four. Okay. This is the final answer of the question. Thank

Eso won and graft this equation already be careful. Sonata functions You don't wanna say that. And then X equals zero is just the y axis. You get a visual there, and what's important is you want to see that the bounds that where they cross are from negative one, they do cross at zero. But I'm not gonna do that with my integral show. You a way around that, um, and positive one. And the reason why I'm going to ignore that is I just copy this equation real quick if I were to create a new equation, but right as the absolute value of that function, you can actually type into your calculator so the areas will not cancel each other out. Eso then all you'd have to do is find your integral key, which mines under the functions miscellaneous and egg roll from negative one to one of the absolute value of that function. And then you after I d y, um, and you get the exact answer of only five. Just so you know, there's other ways of doing this. If I hide that function and go back to this, um, some of you might be saying there. What if you go from negative 120 You can absolutely no 1 to 0. But think about. Okay, well, we want the area between the Kurds and areas always positive. So then double that. That's why those areas you do not want to cancel out family was thinking that, um ah, and you can actually do the integral of this. It's 1/4 y to the fourth minus one half life squared and plug in one and negative one and see that you'll get possible in half. I feel like I've over explained this problem to this point, so hopefully you're happy with what I've said so far.

In the kitchen. It is asking to find the area under the given graph function that is effect is equal to X. Times of E. To the power minus X from X is equal to 0 2. X is equal to three. So by this data I have to find the area. So finding 85 for finding area it will be returned as that is area will be equal to yeah integral 0 to 3 X. E two. Department X. D X. So first I have to find this definite integral. Then I get the value of area easily. So that assumed that U. Is equal to X. So do you will become that is equal to dx. And let's assume again that D V is equal to eat department X Dx. So we will be after integrating value each minus here to the power minus cells. No, my next issue is applying there formula of integration by part which is written as integral. You D V will be equal to UV minus integral V D U. So this is the formula of integration by part was substitute all the about data in this formula So this is after some shooting it will be bitterness integral. UDV means us x and DV s minus into the power sorry into the power plus into the power minus x dx is equal to ue means x times of minus it'll depart minus x minus integral. We miss minus E to depart minus x. D humans dx no simplify this. Then I can say that integral X into the part -X DX will be equal to -1 times of you to depart minus x minus minus become plus integral E to the power minus x D x. It's simplify this again. Then I can say that integral X times of E to depart minus x D x will be equal to minus X. You to depart minus x minus E. To the power After integrating it'll depart minus x. Dx will be minus, it will depart minus x plus C. No S U C. The given limited here I had find the value of integral ex He'll eat depart minus x dx. The value which I get in desert. So no, I am applying the limits. Okay, so I can say that 0 to 3 integral X. Times of E. To the power minus X. D X will be equal to record. Open minus X. E. To the power minus x minus 24 minus x bracket Bracket closed 0- three. No after applying the limits by using the phenomenal theorem of calculus, the value will be equal to it is minus three times of it. To the poor Monastery minus eight. To the power minus three minus minus minus become plus zero, multiplied by 18 point minus zero will be zero minus minus minus become plus into the power minus zero knows all this. Then I will get the value of area that is equal to 0 to 3 X. Times of a. To the power minus x. D x will be equal to -3 times of way to depart -3 minus lead to depart minus three plus one. So final value is that is minus four times of a to depart minus three plus one. So this is the value of Area 88. Hence I had to get the value of area Which is equal to 4 -4 times of it'll depart -3 plus one. So I had sold occasion. Thank you.

The reason. Even ambiguous and white, one minus X expert. Well, you can do the area under the given occur and above the exit. So as you know, the formula for the area, it magical. It would be why BX there extended far into unit. It's maybe were I. It will be pastorally company. The value of any so Baylock envy will compel the X intercept off the given. So the for computer, the X intercept for the given Cup blocked by plugging the white people, would you? So why different? Geo one minus X squared. So excess critical one. The value of X is last. Mannesmann So valuable age we can I hear daily walk a minus one in the value of beach. We'll know a lot in here. So the minus one well, the video of quiet one minus its the spread and do be now inventing is an indication of one X, and then they get enough excess guy and in the power of very indicates an excuse. But a kiddie limited minus one. Do what now? Most people like that, like in the parliaments of the Apple Limited one minus one Q by TD minus minus one minus minus one. Can you buy TV from here? We get one minus one between. Good to wait. TD minus minus one minus a leg minus minutes. Mess plus or minus minutes. Plus to the minus one. Last one day. No, simply pay more than you get. Who by T minus minus one plus on Betty's minus two Bay Hill. Now we wait three minutes minutes, plus so plus to obey team. It's now at the base close to Betty. Then they'll get the ideological do a magical before. Wait till so the final answer is for right. Thank you.


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