Calculus

posted by .

so we are doing integrals and I have this question on my assignment and I can't seem to get it, because we have the trig substituion rules, but the number isn't even so its not a perfect square and I just cant get it, so any help would be greatly appreciated. The question is :

integral of du/ (u*sqrt(4-u^2))

Thanks again

Use the concept of U substitution!

--Becky Meyers, Harvard Class of 2011

We have to use Trig substition before we can use U substution because it won't work the other way, I tried, I know what the answer is supposed to be I just can't get it.

integral of du/ (u*sqrt(4-u^2))

Substitute u = 1/t. Then

du = -dt/t^2

u*sqrt[4-u^2] = 1/t sqrt[4-1/t^2]

du/ (u*sqrt(4-u^2)) =

-dt/t^2 * t/sqrt[4-1/t^2] =

-dt/[t sqrt(4-1/t^2)] =

-dt/sqrt[4 t^2 - 1]

So, you should do a hyperbolic substitution:

put t = 1/2 cosh(y)

then

dt = 1/2 sinh(y)


sqrt[4 t^2 - 1] = sinh(y)


-dt/sqrt[4 t^2 - 1] = -1/2 dy

The integral is thus y/2 + c =

arccosh(2t) + c =

arccosh(2/u) + c =

Log[2/u + sqrt(4/u^2 - 1)] + c =

Log[2 + sqrt(4 - u^2)] - Log(u) + c =

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Physics

    when we do convertions, do we have follow the rules for rounding?
  2. math, algebra

    How is 28 a perfect number? Can someone explain this to me. all i understand that all perfect numbers end in 6 and 8. But how and why is 28 a perfect number. dimes are packaged 50 in a roll. quarters come 40 in a roll.susan b anthony
  3. calculus

    how do you calculate the instantaneous rate of change. is that the derivative. also: if f is the antiderivate of (x^2)/(1+x^5 such that f(1)=o then f(4)=?
  4. Algebra

    what is a perfect square number i know 9, 25 and 100, but what else if you multiply a perfect square by a perfect square, is the answer always a perfect square
  5. calculus

    [integrals]2/tsqrt(t^4+25) integrals of two over t square root of t to the 4th plus 25
  6. math

    The number 1 is a perfect square (1X1=1) and a perfect cube (1X1X1=1). What is the next smallest whole number which is both a perfect square and a perfect cube?
  7. Math

    Which numbers are perfect squares? A) 64 b)900 c)120 d)1000 e)100 F) 10 000 How do u know each number is a perfect square?
  8. MATH PLEASE HELP

    Thank you very much for the answer stated below: A perfect square will have an even number of repetitions of each prime factor. 180 = 2*2*3*3*5 e have 2^2 and 3^2, but we need another 5. So, 180*5 = 900 = 30^2 = (2*3*5)^2
  9. Calculus

    Integrate [1/square root of(e^(2x)-1)]. I have to use u substitution. We are doing the integrals of inverse trig functions, but I cannot get it to work out!
  10. math

    I have a question on a quiz, and I cant seem to figure it out I have to add 50,56,52,46,48,42,38 and that got me 332 then I have to divide it by 7 and get the mean, but then I get a remainder of 3 and I don't know what to do because …

More Similar Questions