calculus

how to take the integral of cos(square root of x) dx.
need to use substitution and integration by parts but I don't know what to substitute

  1. 👍
  2. 👎
  3. 👁
  1. let t = x^.5
    dt = .5 x^-.5 dx
    so dx = 2 x^.5 dt which is dx = 2 t dt

    so integral of 2 t cos t dt

    that might help

    1. 👍
    2. 👎
  2. (Integral of) cos x^(1/2) dx
    Do the substitution part first.
    Let x^(1/2) = y
    x = y^2
    dx = 2y du
    So the integral becomes, after substitution
    2*(Integral of)y cos y dy
    Now use integration by parts. You may have to use it twice.
    You should end up with
    2 cos y + y sin y
    Then substitute back x in terms of y
    = 2 cos(sqrt x) + 2sqrt x * sin(sqrt x)

    1. 👍
    2. 👎
  3. integral of 2 t cos t dt

    let u = 2 t
    so du = 2 dt
    let dv = cos t dt
    so v = sin t

    u v = 2 t sin t

    v du = 2 sin t dt

    u v - integral v du
    = 2 t sin t + 2 cos t

    1. 👍
    2. 👎
  4. Remarkable :) LOL

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. Math ~CHECK MY ANSWER~

    1) Which of these is a rational number? a. Pi b. Square root 3 ****** c. Square root 2 d. 1.3 (the # 3 has a line at the top) 2) Which of the following sets contains 3 irrational numbers? a. Square root 120 , n , Square root 3

  2. ALGEBRA

    1, Factor each expression x^2 - 10x - 24 A. (x + 4)(x - 6) B. (x + 6)(x - 4) C. (x + 2)(x - 12) D. (x + 12)(x - 2) 2, x^2 - 36 = 0 A. (1 + square root of 3, 1 - square root of 3) B. (-6,6) C. No solution D. None of these 3, Factor

  3. Calculus

    What is the best substitution to make to evaluate the integral of the quotient of cosine of 2 times x and the square root of the quantity 5 minus 2 times the sine of 2 times x, dx? u = sin(2x) u = cos(2x) u = 2x u = 5 − 2sin(2x)

  4. algebra

    1)Write the expression 9n^6+7n^3-6 in quadratic form,if possible A.9(n^3)^3+7n^3-6 B.9(n^2)^3+7(n^2)-6 C.9(n^3)^2+7(n^3)-6 D.not possible I'm thinking C on this one but im not sure 2)solve b^4+2b^2-24=0 A.-2,-square root of

  1. Tirginometry

    the expression 4ab(square root of)2b-3a(square root of)18b^3+7ab(square root of)6b is equivalent to... (a)2ab(square root of)6b (b)16ab(square root of)2b (c)-5ab+7ab(square root of)6b (d)-5ab(square root of)2b+7ab(square root

  2. math

    Four students work to find an estimate for square root 37. Who is closest to finding the true estimate? (1 point) Rhonda: "Use square root 16 and square root 25 to estimate." Ricardo: it should be between square root 25 and square

  3. Algebra

    Use the quadratic formula to solve the equation. Give exact answers: 2x^2 -1 = 6x. The choices are: a) -3 + square root(7)/2, -3 - square root(7)/2 b) 3 + square root(11)/2, 3 - square root(11)/2 c) 3 + square root(7)/2, 3 -

  4. help riemann sums

    the expression 1/50 (1/50 +2/50+ 3/50+ .....50/50)is a Reimann sum approximation for (everything in the parantheses is square root except the 1/50 outside the paratheses) the answer has to me the integral form so from looking at

  1. Math Help!

    Which two square roots are used to estimate square root 67? A. Square root 36 and Square root 49. B. Square root 49 and Square root 64. C. Square root 64 and Square root 81. D. Square root 81 and Square root 100. Is the answer C?

  2. Math

    Four students work to find an estimate for square root 27. Who is closest to finding the true estimate? (1 point) Chelsey: "Use square root 16 and square root 25 to estimate." Carley: "I use square root 25 and square root 36."

  3. Calculus

    A rectangle is bounded by the x axis and the semicircle = square root 25-x^2. What length and width should the rectangle have so that its area is a maximum? When I worked the problem out(which is a bit detailed). I started with y

  4. Math Help!

    Four students worked to find an estimate for square root 22. Who is closest to finding the true estimate? A. Tiffany: "Use square root 16 and square root 25 to estimate." B. Todd: "I use square root 9 and square root 16." C.

You can view more similar questions or ask a new question.