Maharashtra State BoardHSC Arts 12th Board Exam
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Evaluate : ∫40(|x|+|x−2|+|x−4|)dx - Mathematics and Statistics

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Evaluate : `int_0^4(|x|+|x-2|+|x-4|)dx`

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Solution

 `int_0^4(|x|+|x-2|+|x-4|)dx`

`I=int_0^4f(x)dx=int_0^2f(x)dx+int_2^4f(x)dx`

`I=int_0^2(x+2-x+4-x)dx+int_2^4(x+x-2+4-x)dx`

`I=int_0^2(x+2-x+4-x)dx+int_2^4(x+x-2+4-x)dx`

`I=int_0^2(6-x)dx+int_2^4(x+2)dx=[6x-x^2/2]_0^2+[x^2/2+2x]_2^4=[12-1]+[8-2+(8-4)]=20`

Concept: Evaluation of Definite Integrals by Substitution
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