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
Oduvanchick [21]
2 years ago
13

Evaluate the definite integral using the graph of f(x) (Image included)

Mathematics
1 answer:
Tanya [424]2 years ago
8 0

a) The first integral corresponds to the area under y = f(x) on the interval [0, 3], which is a right triangle with base 3 and height 5, hence the integral is

\displaystyle \int_0^3 f(x) \, dx = \frac12 \times 3 \times 5 = \boxed{\frac{15}2}

b) The integral is zero since the areas under the curve over [3, 4] and [4, 5] are equal but opposite in sign. In other words, on the interval [3, 5], f(x) is symmetric and odd about x = 4, so

\displaystyle \int_3^5 f(x) \, dx = \int_3^4 f(x) \, dx + \int_4^5 f(x) \, dx = \int_3^4 f(x) \, dx - \int_3^4 f(x) \, dx = \boxed{0}

c) The integral over [5, 9] is the negative of the area of a rectangle with length 9 - 5 = 4 and height 5, so

\displaystyle \int_5^9 f(x) \, dx = -4\times5 = -20

Then by linearity, we have

\displaystyle \int_0^9 f(x) \, dx = \left\{\int_0^3 + \int_3^5 + \int_5^9\right\} f(x) \, dx = \frac{15}2 + 0 - 20 = \boxed{-\frac{25}2}

You might be interested in
The original price of a mirror was priced at $15 but was on sale. The amount of the discount is $3. What percent is the discount
Sloan [31]

Answer:

20%

Step-by-step explanation:

You do 3 divided by 15 which is 0.2, or 20 percent.

5 0
2 years ago
-8(p - 4) = 96 solve for p
Gwar [14]

Answer:

-8

Step-by-step explanation:

3 0
3 years ago
Ann, Claire, and Josh collect stickers. One week, Ann collects 7 more stickers than Josh. Josh collects twice as many stickers a
UkoKoshka [18]

Answer:

Claire = 30 stickers

Josh = 60 stickers

Ann = 67 stickers

Step-by-step explanation:

Let

Claire stickers= x

Josh = 2x

Ann= 2x + 7

Total stickers = 157

Total stickers = Claire stickers + Josh stickers + Ann stickers

157 = x + (2x) + (2x+7)

157 = x + 2x + 2x + 7

157 = 5x + 7

Subtract 7 from both sides

157 - 7 = 5x + 7 - 7

150 = 5x

Divide both sides by 5

150/5 = x

30 = x

x = 30

Claire stickers= x

=30 stickers

Josh = 2x

= 2(30)

= 60 stickers

Ann= 2x + 7

= 2(30) + 7

= 60 + 7

= 67 stickers

Claire = 30 stickers

Josh = 60 stickers

Ann = 67 stickers

6 0
3 years ago
Solve for b.<br> 3-2(b - 2) = 2 - 7b
malfutka [58]

Answer:

b = -1

Step-by-step explanation:

use distributive property to multiply the -2 with the numbers in the parentheses

3 - 2b + 4 = 2 - 7b

7 - 2b = 2 - 7b

add 2b to both sides

7 = 2- 5b

subtract 2 from both sides

5 = -5b

divide by -5

b = -1

5 0
3 years ago
Read 2 more answers
Solve for x. A.x=7.5 B.x=16 C.x=17.5 D.x=27.5
dedylja [7]
You can't solve for x. There is nothing more you can do to the equation. Are you sure your solving for x?
6 0
3 years ago
Other questions:
  • Rewrite each expression using the distributive property. Then combine like terms if possible. 2(x+4
    14·1 answer
  • Ian and his brother are driving from city A to city B. The two cities are 282 miles apart. Ian drives at 47 miles per hour. How
    15·1 answer
  • Let f(x)=x^2+5 and g(x)= (x+5)/x find (g fog f)(-3)
    15·1 answer
  • Give an example of a defined term and explain what is defined.
    11·1 answer
  • If tanA = 1/2 then evaluate cos A/sinA +sinA /1+cosA​
    10·1 answer
  • What is the slope of this line?
    7·2 answers
  • Trigonometry can anyone help me out
    14·2 answers
  • A projectile travels 1,440 feet per second. How fast is the projectile in miles per hour?
    12·2 answers
  • Angelina deposits $3000 in a savings account on 1 January 2019, earning compound interest of 1.5% per year.
    15·1 answer
  • 100 grams/day of substance x is filtered, 50 grams/day is reabsorbed, 75 grams/day is secreted and 125 grams/day is excreted. su
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!