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Question:

justinbains132
justinbains132
Student
High School - 12th Grade

Let f(x)= 4-3x. Find K so that the integral from -1 to x of f(t)dt+k = the integral from 3 to x of f(t)?

Also find d/dx the integral from -1 to x f(t)dt

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Posted by justinbains132 on Sunday May 10, 2009 at 1:46 PM and tagged with calculus, integrals, math.

Answers:

  1. jkj1362
    jkj1362 Teacher

    justinbains132,

    the intergral from -1 to x of f(t)dt+k is

    (-3/2)*x^2 + (4 + k)*x + 11/2 + k

    the integral from 3 to x of f(t) is

    (-3/2)*x^2 + 4x + 3/2

    These two values are equal, so

    (-3/2)*x^2 + (4 + k)*x + 11/2 + k = (-3/2)*x^2 + 4x + 3/2

    If we simplify this equation,

    k*x = -k - 4

    If we solve this equation to k,

    k = 4/(x+1)

    d/dx the integral from -1 to x of f(t)dt is

    4 -  3x

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    Posted by jkj1362 on Sunday May 17, 2009 at 7:46 PM

  2. neela
    neela Teacher
    Graduate School

    eNotes Editor

    Integral of 4-3x between -1 to x is ( 4x-3x^2/2) at x-( 4x-3x^2/2) at x=-1  with k added is  4(x+1)-(3/2)(x^2-(-1)^2)+k-------(1)

    The integral  between 3 to x  is 4(x-3)-(3/2)(x^2-3^2)-----(2)

    From (1) and (2) by equating,and simplifying,

    4x+4-(3/2)x^2 +3/2 + k= 4x-12+(3/2)x^2+27/2. Canceling the same appearing on both sides, we get,

    4+3/2+k=-12+27/2 or

    k=-4.


    Integral from -1 to x of f(x)dx is 4x-(3/2)x^2 is 4-3x^2+ K=-3

    Therefore,  d/dx of {4x-(3/2)x^2) +k} = 4-3x+0 = 4-3x.

     

     

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    Posted by neela on Friday June 5, 2009 at 3:00 AM