solve-the-given-problems-show-that-int_01-x3-d-xint_12-x3-d-xint_02-x3-d-x-in-terms-of-area-explai-3

Question

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.

Dwijendra Rao · Accepted Answer

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&#x27;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.

Ramzi Deek · Answer

So we got integral of 0 to 1 of X times three to the X squared plus one DX. So we know that you is X squared plus one Do you over DX is two x So do you over to X is the X. So I start playing in 0 to 1 of X times three to the u through the power of you times do you over two x So these two X&#x27;s cancel. We can also factor half outside. So that&#x27;s half into girl 01 have three to the U do you? So that&#x27;ll be so half times three to the u over Ln of three. So that&#x27;s three to the U over Ln of three. So no, let&#x27;s plug in X square plus one here. So that&#x27;s three to the X squared plus one over to Ln of three. Now we need to plug in 0 to 1 10 here, so that will be three squared over two Ln three minus three over to Ellen of three. So that will give us so nine minus three. That would give you six. Your final answer is six over to Ellen, three

Matt Just · Answer

I don&#x27;t know. We have the definite integral zero two four of minus X to the three halves plus x to the one half d x. I could start by finding an anti derivative. So we have so this minus Khun stay are here. And then the entire derivative is so we add one to the exponents We get X to the five hands over five hands plus x to the three halves over three. House evaluated from zero to four. Okay. And so four to the five halves We&#x27;LL take the square root and then take the fifth power. So it&#x27;s two to the fifth, which he be thirty two over five halves plus okay. Squared two cubes of eight over three halves and then minus this evaluated your over that Syria. Okay, so, uh, this is minus can multiply by their sim prickles of both the numerator is get doubles at sixty for over five plus sixteen over three and so we need to get a common denominator. I mean, we could leave it like this, but if we do get the common denominator of fifteen, you should get negative. Six fifty six. Divided by fifteen is the final answer

Xiaomeng Zhang · Answer

So those one dressy coast through my nose three times acts to power off, Serie over to and miners into grow off access to the power off house. Okay, so for our 1st 1 that a cow shoe True over five times, actually. Power are 5/2 40 and my noticed us to over three times acts to the power off. 3/2, full zero. So for the 1st 1 that they go to six. So our five I&#x27;m too through the power off five that is 32. And for those one, we have to over three times, two to the power off street so we can see that he has to six times or be too. And that&#x27;s why he goes to 16/3. So we&#x27;re have the answer. You kill two minor 65 6/15

Audrey Fong · Answer

we want to integrate dysfunction before we do that. Let&#x27;s spin. So I have X squared minus six x last night has spent the Xing I have execute minus six X square last night x using basic integration rule I have X for willful minus six x cubed over three less my ex Square public too. And that would give me explore four minus two x cute less night over two x way subbing in the upper low Willing me, I would have won Quokka minus troop last night over to minus zero minus zero plus zero. Final answer is 11 over for

Fuzail Shakir · Answer

Okay, So for this, we have the integral from negative 1 to 1 off. Three linus to x times t x So this is equal to the integral from negative 3 1 to 1 of three d x minus the integral from negative 3 1 to 1 off to x t x. So this interview on the left is equal to three X evaluated from negative 3 1 to 1 minus X squared, evaluated from negative. Want one. So three acts evaluated from negative 1 3 1 to 1 is just three minus negative. Three. All right. Minus X squared. Evaluated from negative. Want one is just equal to one minus one. So this part goes to zero and this part goes to three plus three equals six.

Problem

Solve the given problems. Write $\int_{1}^{8} f(x…

Problem 35 Easy Difficulty

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.

Answer

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