David Young

2021-12-30

Calculate the integral.

${\int}_{1}^{3}|2x-4|dx$

Fasaniu

Beginner2021-12-31Added 46 answers

Step 1

Consider the provided integral,

${\int}_{1}^{3}|2x-4|dx$

Evaluate the provided integral.

The our function is defined at the point 2.

a<b<c : f(b)=undefined

So,${\int}_{a}^{c}f\left(x\right)dx={\int}_{a}^{b}f\left(x\right)dx+{\int}_{b}^{c}f\left(x\right)dx$

Therefore,

${\int}_{1}^{3}|2x-4|dx={\int}_{1}^{2}-2x+4dx+{\int}_{2}^{3}2x-4dx$

Step 2

Simplifying further,

${\int}_{1}^{3}|2x-4|dx={\int}_{1}^{2}-2x+4dx+{\int}_{2}^{3}2x-4dx$

$=-{\left[{x}^{2}\right]}_{1}^{2}+4{\left[x\right]}_{1}^{2}+{\left[{x}^{2}\right]}_{2}^{3}-4{\left[x\right]}_{2}^{3}$

=-[4-1]+4[2-1]+[9-4]-4[3-2]

=-3+4+5-4

=-3+5

=2

Hence.

Consider the provided integral,

Evaluate the provided integral.

The our function is defined at the point 2.

a<b<c : f(b)=undefined

So,

Therefore,

Step 2

Simplifying further,

=-[4-1]+4[2-1]+[9-4]-4[3-2]

=-3+4+5-4

=-3+5

=2

Hence.

trisanualb6

Beginner2022-01-01Added 32 answers

Lets

Vasquez

Skilled2022-01-07Added 457 answers

Transform

Evaluate

1+1

Answer:

2