Find the definite integral from 1 to 3 of |-3x+1|

Edmund Conti

Edmund Conti

Answered question

2021-11-14

Find the definite integral from 1 to 3 of |-3x+1| dx

Answer & Explanation

Feas1981

Feas1981

Beginner2021-11-15Added 16 answers

Step 1
According to the given information it is required to find the value of the definite integral.
13|3x+1|dx
Step 2
|x|={x if x>0x if x<0
Step 3
Since x > 1 so,
13|(3x1)|dx=13(3x1)dx
Step 4
Now, solve the integral:
13(3x1)dx=133xdx131dx
=[3x22]13[x]13[usingab(f(x)+g(x))dx=abf(x)dx+abg(x)dx]
=32(91)(31)
=3(4)-(2)
12-2
=10
Step 5
Therefore,
13|3x+1|dx=10

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