calculus

Evaluate integral of e^x^(1/2) / x^(1/2)
I've looked at the answer but I don't understand what people do in their steps.

When I substitute x^(1/2) for u, I get:

2du = 1/x^(1/2) dx

But what do you do with the 1/x^(1/2) dx? It just disappears in the solutions I've seen people give.

  1. 👍 0
  2. 👎 0
  3. 👁 104
  1. yes. the substitution is correct:
    let u = x^(1/2)
    thus du = 1/[2(x^(1/2))] dx, or
    dx = 2(x^(1/2)) du, or
    dx = 2u du
    substituting these to original integral,
    integral of [e^x^(1/2) / x^(1/2)] dx
    integral of [(e^u) / u] * (2u) du
    the u's will cancel out:
    integral of [2*e^u] du
    we can readily integrate this to
    2*e^u + C
    substituting back the value of u,
    2*e^(x^(1/2)) + C

    hope this helps~ :)

    1. 👍 0
    2. 👎 0
    posted by Jai
  2. This helped alot :)

    1. 👍 0
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. calculus

    a) Let f(z) = z^2 and γ(t) = 1 + it^3, t ∈ [0,1]. i) Write out the contour integral ∫γ f(z)dz as an integral with respect to t. You do not need to evaluate this integral. ii) Evaluate the integral ∫0,1+i z^2dz iii) What is

    asked by jack on March 5, 2016
  2. Calculus

    1. Express the given integral as the limit of a Riemann sum but do not evaluate: integral[0 to 3]((x^3 - 6x)dx) 2.Use the Fundamental Theorem to evaluate integral[0 to 3]((x^3 - 6x)dx).(Your answer must include the

    asked by Ernie on May 7, 2018
  3. Math

    Let A denote the portion of the curve y = sqrt(x) that is between the lines x = 1 and x = 4. 1) Set up, don't evaluate, 2 integrals, one in the variable x and one in the variable y, for the length of A. My Work: for x:

    asked by Daisy on January 25, 2017
  4. Math

    1. Evaluate the indefinite integral ([6x^2 + 12x^(3/2) +4x+9]/sqrt x)dx. Answer = + C 2. Evaluate the indefinite integral (12sin x+4tan x)dx. Answer = + C 3. Evaluate the indefinite integral. (x^7)e^(x^8)dx. Answer = + C Thank you

    asked by Matt on September 19, 2011
  5. calculus

    Suppose R is the rectangle 1

    asked by Bryant on March 18, 2012
  6. Math. Need help

    1.if g=5 and k=1, evaluate 9+gk a. 13 b. 14 c. 15 d. 16 2.Evaluate a-b^2/b if a = 10 and b = 2. a. 1 b. 3 c. 8 d. 32 3.Evaluate 3xy^2 - y if x = 2 and y = 5. a. 26 b. 30 c. 120 d. 145 4.Evaluate 2d + d^2/3 if d = 6. a. 4 b. 12 c.

    asked by A. on August 28, 2016
  7. statistics

    I don't understand how to answer this: relate the three measures of central tendency to a normal distribution- I looked it up online and it said that the mean, median, and mode are all the same but i don't understand how that can

    asked by katie on February 12, 2009
  8. Calculus

    Evaluate integral, don't use calculator. I'll use the S as the sign for integral S 4 sin (theta)d(theta) from pi/2 to pi I know the answer is 4 because I enter it in on my calculator, but don't know the steps to get to the answer.

    asked by Janet on May 9, 2011
  9. calculus

    8). Part 1 of 2: In the solid the base is a circle x^2+y^2=16 and the cross-section perpendicular to the y-axis is a square. Set up a definite integral expressing the volume of the solid. Answer choices: integral from -4 to 4 of

    asked by Sally on April 14, 2013
  10. Calculus

    Hello. I would appreciate it if someone could check my answers. I'm sorry it is so long. 1.) Let R denote the region between the curves y=x^-1 and y=x^-2 over the interval 1

    asked by Shay on September 3, 2005

More Similar Questions