1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Aloiza [94]
3 years ago
8

Evaluate the integral ∫2−1|x−1|dx

Mathematics
1 answer:
defon3 years ago
5 0

I think you might be referring to the definite integral,

\displaystyle \int_{-1}^2|x-1|\,\mathrm dx

Recall the definition of absolute value:

|x| = \begin{cases}x&\text{if }x\ge0\\-x&\text{if }x

Then |x-1|=x-1 if x\ge1, and |x-1|=1-x is x. So spliting up the integral at <em>x</em> = 1, we have

\displaystyle \int_{-1}^2|x-1|\,\mathrm dx = \int_{-1}^1(1-x)\,\mathrm dx + \int_1^2(x-1)\,\mathrm dx

The rest is simple:

\displaystyle \int_{-1}^2|x-1|\,\mathrm dx = \left(x-\dfrac{x^2}2\right)\bigg|_{-1}^1 + \left(\dfrac{x^2}2-x\right)\bigg|_1^2 \\\\ = \left(\left(1-\frac12\right)-\left(-1-\frac12\right)\right) + \left(\left(2-2\right)-\left(\frac12-1\right)\right) \\\\ = \boxed{\frac52}

You might be interested in
Atilio solved 3 x 5 x 2 using the equations below.
Diano4ka-milaya [45]

Answer:

3×5×2

= 3×(5×2)

= 3×10

= 30

8 0
2 years ago
Center is at C(-4,6) and is tangent to the x-axis
olya-2409 [2.1K]

Answer:

Lol ..... I don't know the answer :D :P

Step-by-step explanation:

L.H.S x 0 = 0

R.H.S x 0 = 0

L.H.S = R.H.S

Hence , proved .....

6 0
3 years ago
Rounded to the nearest tenth, what is the length of LN? sin(20°) = LN/8<br> (8)sin(20°) = LN
blagie [28]

Answer:

2.7

Step-by-step explanation:

8 * sin(20) = 2.736

8 0
3 years ago
Henry spent 1 hour 30 minutes less than Joey reading last week. Joey spent 50 minutes less than Pete. Pete spent 3 hours reading
Nookie1986 [14]

Answer: Henry read for a total of 40 minutes

Step-by-step explanation: 3:00 - 0:50 is 2:10 then 2:10 - 1:30= 40 minutes

3 0
3 years ago
Read 2 more answers
The vertices of a parallelogram are at (4, 1) , (10, 1), (8, -4) , and (2, -4). What is the area of the parallelogram
Margarita [4]
I think the area is 30 units
8 0
4 years ago
Other questions:
  • The difference between -87 and -125.62?
    15·1 answer
  • Mr. Lee left his fortune to his 3 sons, 4 daughters and his wife. Each son received twice as much as each daughter and his wife
    15·1 answer
  • It is called a _____ when members of the population are chosen because they are easily accessible
    6·2 answers
  • Solve. x^2 8x 25 = 0
    7·1 answer
  • 3 x + 5 = 11<br>Proceso:<br>• Verificación:<br>• Conjunto Solución:​
    9·1 answer
  • How do you round numbers?​
    15·1 answer
  • What is half of 1/4 and half of that half?
    14·1 answer
  • In 2015, Macon County had a population of 53,792. The population increases by 2.5% annually. Which function can be used to model
    10·1 answer
  • According to your budget forecast you will have expenses of $1,200 next month and income of $800. How much do you have available
    5·2 answers
  • A)A certain clothing company employs machinist and supervisors. The company uses the formula y =35x +1 to determine the number o
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!