Question
(6) (a) Evaluate 0 the indefinite, Tp integrals No simnplification 2 answers required.
(6) (a) Evaluate 0 the indefinite, Tp integrals No simnplification 2 answers required.
Answers
7-46 Evaluate the indefinite integral.
$\int \frac{d x}{a x+b} \quad(a \neq 0)$
A question off a person like this, you know, do. Bye Bye. Six. And here it is. DX a boon. One minus Sign to work. If we can hurt all the part in the top 10 as we know it. Well, sign next will be to 10 x upon one place. Dennis Quaid. Finally, it will be change 56 DX one minus 2 10 x by one plus Dundas Square. If we take as I equal do you're five Essex and in new picture, It could be six. Glad x, TX narratives. What does Dennis Clinic minus 10 X Scully. It is part off. It is part off one minus 10 X bullet square. Now let one minus 10 x as d six square X DX with negative sign will predating. Now it's in the little X equal to zero develope. What an ex Acquittal five Essex do you will be one minus went by. Hence question will convert as when a bone one minus one by negative. Same duty upon the square for t minus stupidity and a filler. Just negative sign. Hold three minus one by 13 Here it is. Final part run by T and 12 again. You will be minus sign. So three minus one by so for take minus well minus. They told me by my name. It feel my reply. This two part there were three by three minus one in tow.
Again discussion. We have to solve integration. X squared dx and the limit is 0 to 6. Okay, so first of all in this question, we will solve the integral part here. And then we will apply the limits. Okay, So the integration 0 to 6 x squared DX. It will be the integration of access square. Will be. I'm writing down here. The integration of access to the power and the exit will be expressed to devour n plus one divided by one plus one plus c. Okay, So it will be expressed to the power to plus one divided by two plus one. And we will not apply the constant here because we have the definite limits here. That is 0 to 6, and it will be X cubed, divided by three. And the limit is 0 to 6. Okay, Now we will apply the limits and it will be won by three. First of all, upper limit. That is X cubed minus one by three. It is zero Q. Okay. And it will be six cubed, divided by three. Because this portion will be zero. Okay, so it will be 6.6 dot six divided by three, it will be, too. And that will be 72. So we can say the integration of X squared DX from 0 to 6. It will be 72. And this will be our final answer. Thank you.
In this problem. First time integrating the value with respect to X considering why edge constant so I can write the integration and integration 0 to 2 xq bye bye t from zero to wise choir d by simplifying it further, I can write devaluate 0 to 2. Why? To the power seven by three d y, which is equal to one by three. Why do the power it by to the why to the power eight by eight from judo to to on going forward and simplifying it further. So I get the value edge one by 20 for multiplication and 256 which is equal to 32 by three. So this is our answer.
I can write the given integration edge integration 0 to 1 be because as cube from zero to Esquire Bs simplifying it further I can I've 0 to 1 integration as it squad because as cube minus zero ds on further solving I can write Evaluate you go to one as the square multiplication cause Ask you bs on further going now latest take ask you is equal to you So three years is square ds will become the you so access square D s is equal to one by three Do you now? When I extend to zero, you tend to zero So when ash tends to one, you don't tend to one. Therefore the question can be written edged integration of 0 to 1 cause you BU by three on further solving I can write devaluate one by three integration of 0 to 1 because you d which is equal to one by three multiplication Sign you from 0 to 1 which is equal to one by three Sign one minus zero On further solving I get the value edge one by three Sign one This is our answer