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Solve the given problems.Show that $\int_{0}^{1} x d x>\int_{0}^{1} x^{2} d x$ and $\int_{1}^{2} x d x<\int_{1}^{2} x^{2} d x .$ In termsof area, explain the result.

Calculus 1 / AB

Chapter 25

Integration

Section 4

The Definite Integral

Integrals

Missouri State University

Baylor University

University of Michigan - Ann Arbor

Boston College

Lectures

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In mathematics, precalculu…

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Show that $\int_{0}^{1} …

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Evaluate the following int…

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Evaluating integrals Evalu…

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calculate the integral. $$…

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00:25

Evaluate the integral by i…

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04:25

$$\text {Evaluate the foll…

Hello Friends. We have to solve the problem. We have to solve that 0-1 of X. Dx is greater than 0- one Off Access Code. The X. Okay. And 0122 of x. dx isn't isn't 1 to 2 of X squared dx. Okay. Visual interrogate. If you can't do. Yeah. We will integrate eggs. So this will be access square by two. 0 to 1 Is greater than X. Qy three As you know the one X Square by two or 1- two. Loser. Excuse by three. I want to do so this will leave when we do is greater than one battery here. This will be Trevor do. It's lesser 713 Mhm. Yeah. Because we know that the graph of the X square end X. This is the graph of access square and this will be the glove off. Yeah. X. Okay. This point is one. This is zero. This is why access and this is X. X. S. Okay. Yes. Okay. You can see that. Mhm. From Exit Quest to 02 x equals to one. The area under the Codify cost two x. From 0 to 1. The area under the curve I cost two X. Is greater than the area under the why costume X. Square. Okay so that's why 0 to 1 X. Of the X. Is greater than 021 X squared dx. Okay. From the limit 1- two. From 1-2 you can see that the area under the curve vehicles to X between X equals to one and actually closer to the area and the car by car. So X. Is less than the area under the car by costume access square. You can see that this is the area under the car. Why close to it's a square if some of this point is. So then the area under the curve. Is this? Yeah you can see that from this graph. Yeah. Mm Yeah. Between X equals 0- one. Yes. The area under the car by close to X is greater than by cost two X squared. Ok, so we can represent it area under the car that is represented by man, Y X of X dx. It is greater than 0 to 1 off excess square dx. Ok. And you can see that between 0 to mhm 12 two. The area under the car From 1- two. Mhm From 1- two. The area under the car by calls to X. It's less than I want to do off the area and access square. Yeah. Yeah. Okay. So this is the answer. I hope your nation. Thank you From the graph. You can also see that and by analytical you can see that by integrating that From 0 to 1. one way to is greater than one x 3. And by integrating X dx from 12 to 3 by two and 1 to 2 of x squared dx seven by through. So seven by three is greater than three by two. So we can see that Yeah, 0 to 1 of X dx is greater than 0 to 1 of the square. The X end 1- two of XDX. Is it wisdom who wanted to off excess square dx? Yeah. So this is the answer. His problem. Yeah. Thank you.

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