1. Questions

Calculus

Find the integral from 0 to 2 of xsqrt(5-sqrt4-x^2)).
The hint said to use substitution of u=sqrt(4-x^2), and that I needed one more substitution, but I don't know how to do it.

  1. 👍
  2. 👎
  3. 👁
Henry

  1. Sorry I forgot the dx after the integral.

    1. 👍
    2. 👎
    Henry

  2. ∫[0,2] x√(5-√(4-x^2)) dx
    Let
    u = 5-√(4-x^2)
    du = x/√(4-x^2) dx
    so, x dx = (5-u) du
    and you now have
    ∫[3,5] √u (5-u) du

    and I'm sure you can handle that, eh?

    1. 👍
    2. 👎
    Steve

  4. Wait, why is it the integral from 3-5 instead of 0-2?

    1. 👍
    2. 👎
    Henry

  5. because now we are using u, not x.
    If, after integration on u, you substitute back into terms of x, then you would use the limits [0,2].

    When x=0, u=3 and when x=2, u=5.

    1. 👍
    2. 👎
    Steve

Respond to this Question

First Name

Your Response

Similar Questions

  1. calculus integrals

    Evaluate the integral by making the given substitution. (Use C for the constant of integration. Remember to use absolute values where appropriate.) integral x^5/x^6-5 dx, u = x6 − 5 I got the answer 1/6ln(x^6-5)+C but it was

  2. Calculus

    If f(x) and g(x) are continuous on [a, b], which one of the following statements is true? ~the integral from a to b of the difference of f of x and g of x, dx equals the integral from a to b of f of x, dx minus the integral from a

  3. Calculus

    Which of the following integrals cannot be evaluated using a simple substitution? the integral of 1 divided by the quantity x squared plus 1, dx the integral of 1 divided by the quantity x squared plus 1, dx the integral of x

  4. math

    Evaluate the following indefinite integral by using the given substitution to reduce the integral to standard form integral 2(2x+6)^5 dx, u=2x+6

  1. Calculus check and help

    Let f and g be the functions given by f(x)=1+sin(2x) and g(x)=e^(x/2). Let R be the shaded region in the first quadrant enclosed by the graphs of f and g. A. Find the the area of R. B. Find the value of z so that x=z cuts the

  2. Calculus Please Help2

    Evaluate the integral by using substitution. Use an upper-case "C" for the constant of integration. integral x^5((x^6-2)^10)dx ty

  3. Calculus

    For the following integral find an appropriate trigonometric substitution of the form x=f(t) to simplify the integral. INT((4x^2-3)^1.5) dx x=?

  4. Calculus

    For the following integral find an appropriate TRIGONOMETRIC SUBSTITUTION of the form x=f(t) to simplify the integral. INT (x^2)/(sqrt(7x^2+4))dx dx x=?

  1. Calculus

    What is the best method to evaluate the integral of 1/(4x^2-9) dx a) Integration by parts b) Rewrite the integral using long division c) Rewrite the integral using partial fractions d) Use a substitution -----> my answer Can you

  2. Calculus (Jacobian question)

    Evaluate double integral ln((x-y)/(x+y)) dy dx where the double integral region is the triangle with vertices (1,0),(4,3), (4,1). Hint: use a transformation with the Jacobian.

  3. Math

    (i) Evaluate integral [ x^3 / (x^2 + 4)^2 ] using trigonometric substitution. (ii) Evaluate integral [ x^3 / (x^2 + 4)^2 ] using regular substitution. (iii) Use a right triangle to check that indeed both answers you obtained in

  4. math

    Note: You can get full credit for this problem by just answering the last question correctly. The initial questions are meant as hints towards the final answer and also allow you the opportunity to get partial credit. Consider the

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