Write the integral as a sum of integrals without absolute

Khaleesi Herbert

Khaleesi Herbert

Answered question

2021-10-27

Write the integral as a sum of integrals without absolute values and evaluate.
05|3x|dx

Answer & Explanation

Faiza Fuller

Faiza Fuller

Skilled2021-10-28Added 108 answers

Step 1
Write the integral as a sum of integrals without absolute values and evaluate.
Step 2
The absolute function f(x)=|3−x| can be written as f(x)={3x0<x<3x3x>3
The integral can be written as 05|3x|dx=03(3x)dx+35(x3)dx.
05|3x|dx=03(3x)dx+35(x3)dx
=[3xx22]03+[x223x]35
=[3(3)3220]+[(5223(5))(3223(3))]
=92+2
=132

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