Explained: "Calculate the integral. ∫13|2x−4|dx"

David Young

Answered question

2021-12-30

Calculate the integral.

\int_{1}^{3} | 2 x - 4 | d x

Fasaniu

Beginner2021-12-31Added 46 answers

Step 1
Consider the provided integral,

\int_{1}^{3} | 2 x - 4 | d x

Evaluate the provided integral.
The our function is defined at the point 2.
a<b<c : f(b)=undefined
So,

\int_{a}^{c} f (x) d x = \int_{a}^{b} f (x) d x + \int_{b}^{c} f (x) d x

Therefore,

\int_{1}^{3} | 2 x - 4 | d x = \int_{1}^{2} - 2 x + 4 d x + \int_{2}^{3} 2 x - 4 d x

Step 2
Simplifying further,

\int_{1}^{3} | 2 x - 4 | d x = \int_{1}^{2} - 2 x + 4 d x + \int_{2}^{3} 2 x - 4 d x

= - {[x^{2}]}_{1}^{2} + 4 {[x]}_{1}^{2} + {[x^{2}]}_{2}^{3} - 4 {[x]}_{2}^{3}

=-[4-1]+4[2-1]+[9-4]-4[3-2]
=-3+4+5-4
=-3+5
=2
Hence.

trisanualb6

Beginner2022-01-01Added 32 answers

\int (2 x - 4) d x

\int (2 x - 4) d x = x^{2} - 4 x

Lets

Vasquez

Expert2022-01-07Added 669 answers

$\int_{1}^{3} | 2 x - 4 | d x$
Transform
$\int_{1}^{2} - (2 x - 4) d x + \int_{2}^{3} 2 x - 4 d x$
Evaluate
1+1
Answer:
2

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