integrate-each-of-the-given-expressions-int-frac4-z-4sqrtz2-2-z-d-z-3

Question

Integrate each of the given expressions.
$$\int \frac{4 z-4}{\sqrt{z^{2}-2 z}} d z$$

Dwijendra Rao · Accepted Answer

Hello Friends. We have to indicate the question they&#x27;re given expression sorry In two years north 40 -4 Upon scurried off the discriminates to use it. 20 of desert. Okay so for the weekend I did Zimmerman is one upon square out of. Yeah. What? This will be their discriminates to set up. They said we will take we will substitute Zebari&#x27;s comments to their why you And we will have translated with respect to Yes. So this will be cost twice over minus of jed one is off to. Sorry? Yeah minus of two. The officer the costume do you so we can add it twice. Of Zimmerman is one of these are the costume do you? So we can die for off. Zimmerman is move on. These are the questions. Two of you will substitute these values in the expressions that this will be questioned. two of the Europe on squirreled off you. Yeah so integration of this will be okay. Your to the power off one is 1 x two do you? So this will be a cost to this world of you upon One way to plus c. So this will be cost 24. He&#x27;s got out of you. Let&#x27;s see. Okay. Yeah. So now we will replace the value of you so that is their discriminates to set four and 2 scuttled off zero is square minus to shed. Let&#x27;s see. So this is a Mhm. On set. Yeah. Mhm. I hope you understood. Thank you.

Aishwarya Krishnakumar · Answer

her problem Number nine, We are also U substitution to find this indefinite. So we&#x27;re gonna let you equal whatever is inside the square root in this case, it b u equals Ford&#x27;s He squared minus five. We can go ahead and take the derivative off both sides. So do you equals a Z D. C. And now we can do the youth substitution. So this equals the integral of the we plug in the U. S. O. B the square root of you instead of all of that. And then instead of the easy easy you plug in do you, However, because do you equals eight DPC because of the eight, we would have to divide this thing I ate. So no, you can take the constant out so that, in this case is the one over eight. And then the integral of the square root of you and the squared of you equals you to the one hash. Anything to the square root is always to the power of one and that makes it easier to find in a girl. Can I get you to the one you? So the interval would be won over eight you to the 3/2 because you would add one over one over three. Let&#x27;s see. And obviously we need to simplify this. So is the won over 12 since he multiplied by two. And then you have a and then you multiply both fractions. And then instead of the u, you have to replace it with this. What you&#x27;ve selected for you or D squared minus hi 3/2 What? See on this would be your final answer.

Amy Jiang · Answer

Okay, so it was here that we have a Z squared insider square root. And if you take the derivative of ZIS grade, he gets some constant time, see, and and easy. So let&#x27;s let you equally, um four z squared minus phi and a number of six derivative of that that gives us four times to set of eight z. Easy. Okay, so we once our, um or do you to be Z and easy. So I&#x27;ll divide by eight on both sides and yet do you over its is equal to see DZ. Okay, I know. Let&#x27;s replace our seas before you. Soviet, um, square roots of four disease squared minus five That&#x27;s square root of Z. It&#x27;s got rid of you and that&#x27;s also used the power of 1/2. And then we have the DZ That&#x27;s do you over eight. Okay. And I want to pull out our 1/8 and then taking the integral yet using a part of 1/2 plus one so that, um, doing over two over grill the two plus c. So what does that give us? That&#x27;s to over eight times to be you to the power of 3/2. I see. Okay, so eight is 42 star. Choose to cancel when I&#x27;m left with a 1/2. We&#x27;re sorry. 1/12 and then you is for Z squared one. It&#x27;s wild to the power of three over to his seat.

Matt Just · Answer

Okay. Another definite integral here in a girl. Negatives, too. Two of four Z plus three casing. But the fundamental theorem of calculus. We just need to find an anti derivative of destruction, which is not hard to see. That&#x27;s justly squared factor of to class three c and then evaluate this from negative to two. So you have to. That&#x27;s two squared plus three times too minus. But the song parentheses too. Times negative. Two squared, plus three times nated too. Okay, so this is eight. And then this is also a divorce attracting. Here we have six minus minus six. So should get Hello.

Xiaomeng Zhang · Answer

so those one dressy co 24 times in Q grow off right last in queue girl office tree so you can see those Why Eco&#x27;s who true? Oh, process, ask wire or two two miners to, And that&#x27;s one dress he comes to three Kratz. And for those one that is four times Truth choir over two that is two and minus two spinal suits. Quirot also be to here, and we can see that&#x27;s one gutsy coast. True, my nose, my nose. To that, it&#x27;s who lost to so that a coast to tell.

Aishwarya Krishnakumar · Answer

So for problem 23 brass to solve this definite integral. And as you can see, we have a lot of square roots and a cube root. So we&#x27;re gonna simplified this. So remember that a square root is equal to the to the 1/2 power and a cube root is he to the 1/3 power? So we&#x27;re gonna use that fact to just simplify the equation so we can get rid of all those square roots. So we have the new girl of 1 to 64 and then if you simplify, this would be the so 1/2 over. See to the 1/3. That would be easy to the 1/6 minus to oversee to the 1/3 which would just be too the to the negative. 1/3 since we don&#x27;t want a fraction as well. So this just makes it easier to find the actual in a girl, and we wouldn&#x27;t have to use u substitution or anything like that. So now all we have to do is find the integral, so you add one. So it would be easy. Seven over six time, six over seven, minus odd one. So it would be easy. 2/3 times three over two and over. Get this too. And you integrate this with respect. Um, to one and 64. So we would have to do Write that up here. And before we find out the answer, we can cancel out these two. And then now we just plug in 64 which is the upper bound 64 and then we subtract the lower bound from it. So the same thing times the lower bound ages one. So if you put this into a calculator, you will get for 47 over seven. This would be the answer.

Problem

Integrate each of the given expressions. $$\int\l…

Problem 35 Easy Difficulty

Integrate each of the given expressions.
$$\int \frac{4 z-4}{\sqrt{z^{2}-2 z}} d z$$

Answer

$4 \sqrt{z^{2}-2 z}+C$

Related Courses

Basic Technical Mathematics with Calculus

Related Topics

Discussion

Top Calculus 1 / AB Educators

Catherine R.

Heather Z.

Caleb E.

Kristen K.

Calculus 1 / AB Courses

Precalculus Review - Intro

Functions on the Real Line - Overview

Recommended Videos

Watch More Solved Questions in Chapter 25

Video Transcript

Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus

Catherine R.

Heather Z.

Caleb E.

Kristen K.

Precalculus Review - Intro

Functions on the Real Line - Overview

What do you need help with?

Textbooks

Ask a question

Courses

AI Tutor

$4 \sqrt{z^{2}-2 z}+C$

Basic Technical Mathematics with Calculus

Catherine R.

Heather Z.

Caleb E.

Kristen K.

Precalculus Review - Intro

Functions on the Real Line - Overview

Allyn J. Washington, Richard S. EvansBasic Technical Mathematics with Calculus

Catherine R.

Heather Z.

Caleb E.

Kristen K.

Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus