David Troyer

2021-12-30

Calculate the integral.

${\int}_{0}^{6}|3-x|dx$

Archie Jones

Beginner2021-12-31Added 34 answers

Step 1

Given:$I={\int}_{0}^{6}|3-x|dx$

for evaluating given integral, we break in two parts and integrate it

Step 2

so,

$I={\int}_{0}^{6}|3-x|dx$

$={\int}_{0}^{3}(3-x)dx+{\int}_{3}^{6}(x-3)dx$

$(\because \int (x-a)dx=\frac{{(x-a)}^{2}}{2}+c)$

$=-\frac{1}{2}{\left[{(x-3)}^{2}\right]}_{0}^{3}+\frac{1}{2}{\left[{(x-3)}^{2}\right]}_{3}^{6}$

$=-\frac{1}{2}[{(3-3)}^{2}-{(0-3)}^{2}]+\frac{1}{2}[{(6-3)}^{2}-{(3-3)}^{2}]$

$=-\frac{1}{2}[0-9]+\frac{1}{2}[9-0]$

$=\frac{9}{2}+\frac{9}{2}$

=9

hence, given integral is equal to 9.

Given:

for evaluating given integral, we break in two parts and integrate it

Step 2

so,

=9

hence, given integral is equal to 9.

Ana Robertson

Beginner2022-01-01Added 26 answers

Step 1

Given:

${\int}_{0}^{6}|3-x|dx$

Step 2

Solution

${\int}_{0}^{3}3-xdx+{\int}_{3}^{6}-(3-x)dx$

Evaluate the integrals

$\frac{9}{2}+\frac{9}{2}$

Calculate the sum

Step 3

Answer:

9

Given:

Step 2

Solution

Evaluate the integrals

Calculate the sum

Step 3

Answer:

9

Vasquez

Expert2022-01-07Added 669 answers

Let's calculate a definite integral:

F(6)=0

F(0)=0

I=6-(0)=6

Answer:

6

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