∫−55 |x+2|dx is equal to

55|x+2|dx is equal to

  1. A

    13

  2. B

    19

  3. C

    21

  4. D

    29

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    Solution:

    Here, the given integrand is in the form of absolute function and we define the absolute function as |x|=x,x0
    or |x|=x,x<0 by using it, we convert the given integrand in simple form and then integrate it.
    Let, I=55|x+2|dx

    It can be seen that (x+2)0 on [5,2] and (x+2)0 on [-2,5]

     I=52(x+2)dx+25(x+2)dx abf(x)dx=acf(x)dx+cbf(x)dx I=x22+2x52+x22+2x25

    =(2)22+2(2)(5)222(5)+(5)22+2(5)(2)222(2) =24252+10+252+102+4=2+4+25210+252+102+4=29

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