Results 1 to 2 of 2
Like Tree1Thanks
  • 1 Post By MarkFL

Thread: Calculus Quiz Problems

  1. #1
    Sep 2018

    Calculus Quiz Problems

    Determine the area of the region enclosed by the graphs of f(x) = x^2 + x +5, g(x) = 3x +13, and the vertical line x = 0

    I got 26.67 but he gave me zero points for it so idk.

    Set up (but do not evaluate) an integral that will give the area of the surface generated when y= x^3/8 is revolved about the y-axis for 3 less than or equal to x, x less than or equal to 4.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor MarkFL's Avatar
    Dec 2011
    St. Augustine, FL.

    Re: Calculus Quiz Problems

    I would begin by plotting the region whose area we are to find:

    Calculus Quiz Problems-mhf_0007.png

    We see the linear function is above the quadratic, and we know the lower limit of integration will be $\displaystyle x=0$. We need to determine where the upper limit is, and that occurs where the two functions are equal for $\displaystyle 0<x$.

    $\displaystyle x^2+x+5=3x+13$

    $\displaystyle x^2-2x-8=0$

    $\displaystyle (x+2)(x-4)=0$

    The positive root is:

    $\displaystyle x=4$

    And to the request area $\displaystyle A$ will be found from:

    $\displaystyle A=\int_0^4 (3x+13)-(x^2+x+5)\,dx=\int_0^4 -x^2+2x+8\,dx=\left[-\frac{x^3}{3}+x^2+8x\right]_0^4=-\frac{64}{3}+16+32=\frac{80}{3}$

    What you cited as the area appears to be a decimal approximation of this same value, rounded to two decimal places, so perhaps that's why you got no credit for it.
    Thanks from harpazo
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Calculus Old Quiz Problems Help
    Posted in the Calculus Forum
    Replies: 1
    Last Post: Sep 20th 2018, 11:07 AM
  2. Replies: 2
    Last Post: Jun 2nd 2010, 07:57 PM
  3. Replies: 4
    Last Post: Dec 9th 2008, 08:29 PM
  4. Wonderful Calculus Quiz problem
    Posted in the Calculus Forum
    Replies: 1
    Last Post: Nov 3rd 2008, 09:10 AM

Search Tags

/mathhelpforum @mathhelpforum