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Solve the given problems.Show that $\int_{0}^{1} x^{3} d x+\int_{1}^{2} x^{3} d x=\int_{0}^{2} x^{3} d x .$ In terms of area,explain the result.

Calculus 1 / AB

Chapter 25

Integration

Section 4

The Definite Integral

Integrals

Campbell University

Harvey Mudd College

Baylor University

Idaho State University

Lectures

03:09

In mathematics, precalculu…

31:55

In mathematics, a function…

02:05

Evaluate the following int…

01:53

Evaluate each definite int…

01:18

01:07

Evaluate the integral.…

00:57

Evaluate the integral by i…

02:28

Calculate the integral.

02:07

01:16

07:06

$$\text {Evaluate the foll…

01:22

Hello friends. We have to solve that given problems we have to do that. The integration of 0-1 XQ of dx plus 1-2 of the rescue of the X Equals to zero. Do indicates enough excuse o of the ex in terms of area explained the result. Okay. So we have to say that. Yeah. So first we will take we know that the the graph of excuse is it something like this? Okay. Support this is .1 and this is 0.2. You know that the integration of any function within the limits represent the area of the car. Mhm. That means 0-1 of x cubed the X. This represent the area of here. He under the car from this point is this is or isn't and this is this point is a this point is be this ponsi and this point is the so this integral represent the area area under the carb that is here he is A or B. Okay. And uh Integration of 1-2 of x cubed li X. This represents the area under the car from A to B. So it is the coastal area of hey baby city. And right inside that is 02 XQ of DX. So this will be equals two area under the car. Between the limit 0- two. So this is Area and that the car between 0-2 that is area half under the curb. Oh, a bee studio. So you can see that from the graph the area of submission of area. Here you are two A. O. D. Plus here he is A B. C. D. You can see that helios. Hey audie plus yeah, hideous area from A. B. C. D. Yeah, it will be because to total area that is from 02 or do Oh A B C. D. Oh baby studio. It is the area under the car, Here, Here, under the car, A O B C D O. So does represent that 0-1 Off excuse Detox and this represented you 1-2 what to do of execute years. So this will be costume from 0 to 2 of yes you do X. This is the explanation of answer in terms of area. I hope you understood. Thank you.

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