use-the-method-of-exercise-51-to-evaluate-the-integral-int-x4-e2-x-d-x

Question

Use the method of exercise 51 to evaluate the integral.
$$\int x^{4} e^{2 x} d x$$

Darshan Maheshwari · Accepted Answer

talk about Question 55. Likewise, we have toe make a table over here and then we have to find its entry derivative for the first column will keep on the appreciating X rays to the ball. Four. So we have four x cubed. I will have Alexa Square will have 24 x will have 24. If you have it is to the board works. We integrate areas to the board. Works over to this will be easy is to the board two weeks or four areas to the board. Two weeks or eight areas to the part two weeks or 16 it is to the board works over 32 Onda Uh, it last we have the science which were toggle between plus minus, plus minus and plus so integral becomes X rays to the poor food it is to eat a support. Works can be fact taken out. So let&#x27;s write. It is to the board to x outside. Inside we have e X rays to the ball forward to minus four times one of the forest one. So we have one way. Have excuse. Just excuse over here, Then we have extra square times 12 or eight, which is three or so we have three or two extra square on were 24/16 which is again three or two. But with the minus sign. So we have minus three or two X. Then we have with the plus sign. That&#x27;s when we come three or four because it will go with aid common which common divisor is a So we have 8/4 on. But then here we have a concert of individual, so this is very quiet answer.

Darshan Maheshwari · Answer

question number 54 again. We need to make a table on. Then we have to find that the derivative. So, uh, the first column will have the derivatives off the differentiation of extras to the 44 So that will be four. Execute. Then we have Alexa Square. Then we have 24 x and we have 24 we&#x27;ll have the integral Zoff areas to the barracks, which will just be areas to the barracks and all the cases. And we are science will switch with Children. Switch between plus minus, plus minus and plus So the integral becomes X rays to the power. Four years to the products TX will be. It is to the bar X times expressed to the ball four minus four x cubed e raised to the bar X plus Bullocks Square E raised the barracks minus 24 x It is to the body X plus 24th it is to the box, plus the constant of diversity. So this is that required Also

Darshan Maheshwari · Answer

this question, we have to gain make a tabular form, just like in question number 51. I mean to finance center derivative. So let&#x27;s first start with column upon, in which we have to differentiate X rays to the power of five. So that would be five X rays to the ball four. That would be 20. Execute. This will be 60 x a square. This will be 1 20 x on this will be 1 20. This is the derivative, Andi. Then we integrate cost Toe x. Okay, So the integral off course to excess sign two x over toe and the girl signed two weeks overdue is minus cause toe works over four. Once again, Integral is a minus. Sign toe works over eight once again will be cost two x or 16 once again would be cause is just science. So we have signed to works over 32 the last one would be minus cause to works over 64. The sign recovered from blood minus, plus minus, plus minus. So this is how the table looks like and we just have to multiply each row and we have to write the integral so the integral becomes X rays to the poor. Five. This will be signed two X. You hear that? We have X rays to the about five times. Signed two x over to, uh, then we&#x27;ll have minus 5/4 X rays to the ball. Four. In fact, minus and minus is plus cause to X minus. 20/8 is nothing but five over to sign towards. And we have a minus sign. Then we have 60/16 extra square cause towards. Then we have a blood sign. 1 20/32 signed two X, and the last one is minus 1 20/64 cause to it. So this is the require integral. We can simplify the ratios a little bit. So if you simplify will get X rays to the power five over to ST Louis. The first three terms mean as a plus, plus five or four straight to the ball for cost to explain this fire over to signed the which now, for 60 or 16 the common divisor, I think, would be forced 14 4, 16. This will be one and five. Here we&#x27;re getting 15 over four Xs square costs to eggs. He will have. I think 8 30 times was 32 8 times. One is eight and this is five. So if you have 15/4, uh, once again, 15/4. Signed two X and the last termers again. Age eight times 80 64 This is one. This is 15 minus 15 over it. Yeah, cause toe X plus the constant of integral. See? So this is the final answer.

Darshan Maheshwari · Answer

Sonoma, 57. Here. Also, we have to make a table toe find into derivative. So then the first column. We have the differentiation of the first job victims or Sex Cube creates a square 66 and six. Then we have here is to the ball Ministry X integral a series to the ball minus three x over ministry. This will be easiest to the ball. Ministry of over nine B e t is to the ball minus two years old, minus 27. And it is to the ball. Ministry of over 81. Yeah, so this is plus minus plus and minus. So if you write the integral let&#x27;s take it is to the par minus three X outside. So we have minus X cube over tree minus x square over tree. Uh, minus. This will be, uh, three times to sixties and 1927 minus 2/9 X and again minus. This is me to over 27 constant, um, less concert over diversity. So this is the required answer

Darshan Maheshwari · Answer

just like question number 51. We have to make a table over here, so let&#x27;s make it. The first column will have their derivatives off the ancient brick, which is expected to call for. So this is three X. So you just will be four x you and will be 12 x will be 12 Over here. We&#x27;ll have the derivative off signs, so he will have minus costs. Then we&#x27;ll have minus sign. Then we&#x27;ll have cause then we&#x27;ll have a sign. And over here we&#x27;ll have a simple, uh, plus and minus signs that part in it. So based on this, uh, die below format are integral becomes minus X rays to the four Cossacks, Then we have plus sign for execute cynics. Then we have another plus sign, uh, one correction. Here, this will be to Alexa Square. You will have 24 x and then we&#x27;ll have 24 so this will be minus cause and this will be plus one more addition, people. Then we&#x27;ll have 12 x square classics. Then we&#x27;ll have minus 24 sine x, and the last time comes out as things will be minus 24 cause thanks plus C. So this is the value of the extras to the ball for Sinus. Indeed, sending

Darshan Maheshwari · Answer

question Number 53. We need to solve this again, using the tabular matter, which is given in the question in question. 51. So in the first column we differentiate X rays to the bar for so we have X rays to the bar for over here we will have four excuse. We&#x27;ll have to. Alexa Square will have 24 X and then we&#x27;ll have our 24 or in the middle column will differentiate cause in this case, differentiation off causes sign So we integrate cause so integral off cause is sign. Can we have minus costs? Then we have minus sine x. Can we have Cossacks? Can we have cynics on the science switch from plus minus plus minus plus So are integral from the stables are integral becomes X rays to the port for cynics, minus and minus is plus four X Q. Call sex minus 12 square sine X minus 24 X Uh, just 24 x koszics. That&#x27;s 24. Hynix? Yes, it&#x27;s a dancer

Problem

Use the method of exercise 51 to evaluate the int…

Problem 55 Hard Difficulty

Use the method of exercise 51 to evaluate the integral.
$$\int x^{4} e^{2 x} d x$$

Answer

$$=\left(\frac{x^{4}}{2}-x^{3}+\frac{3 x^{2}}{2}-\frac{3 x}{2}+\frac{3}{4}\right) e^{2 x}+c$$

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$$=\left(\frac{x^{4}}{2}-x^{3}+\frac{3 x^{2}}{2}-\frac{3 x}{2}+\frac{3}{4}\right) e^{2 x}+c$$

Calculus: Early Transcendental Functions

Grace H.

Kayleah T.

Kristen K.

Samuel H.

Integration Review - Intro

Definite vs Indefinite

Robert T. Smith, Roland B. MintonCalculus: Early Transcendental Functions

Grace H.

Kayleah T.

Kristen K.

Samuel H.

Robert T. Smith, Roland B. Minton

Calculus: Early Transcendental Functions