Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

TomLikesPhysics Group Title

I need help with an Integral (Substitution).

  • 2 years ago
  • 2 years ago

  • This Question is Closed
  1. TomLikesPhysics Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    \[\int\limits_{0}^{100}e^\sqrt{x}dx=?\] I am supposed to solve this using the method of substitution. I have no clue how the hell this would help in that weird case.

    • 2 years ago
  2. hartnn Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    u know integration by parts ?

    • 2 years ago
  3. across Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    Let\[ u=\sqrt x.\tag{1}\]Then,\[ du=\frac1{2\sqrt x}dx\Longrightarrow dx=2\sqrt xdu=2udu.\tag{2} \]It follows from \((1)\) that\[ x=0\Longrightarrow u=0\text{, and}\\ x=100\Longrightarrow u=10. \]So, from \((1)\), \((2)\) and the new limits, we have that\[ 2\int_0^{10}ue^u\,du. \]

    • 2 years ago
  4. TomLikesPhysics Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    @hartnn Yes, that would be my first impulse but I should use the substitution method.

    • 2 years ago
  5. hartnn Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    as shown by @across

    • 2 years ago
  6. TomLikesPhysics Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Ok, and after that I have to integrate by parts do integrate the \[ue^udu\] part, right?

    • 2 years ago
  7. hartnn Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    yes.

    • 2 years ago
  8. across Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    Yes, or you could use the (not so) common knowledge that\[ \int xe^x\,dx=e^x(x-1). \]

    • 2 years ago
  9. TomLikesPhysics Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    ^^ I thought that I saw that Integral before, but not today it seems. Thx for your help.

    • 2 years ago
  10. hartnn Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    more general formula : \(\large \int e^x(f(x)+f'(x))dx=e^xf(x)+c\)

    • 2 years ago
    • Attachments:

See more questions >>>

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.