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
kicyunya [14]
2 years ago
6

Given that 1 x2 dx 0 = 1 3 , use this fact and the properties of integrals to evaluate 1 (4 − 6x2) dx. 0

Mathematics
1 answer:
Debora [2.8K]2 years ago
4 0

So, the definite integral  \int\limits^1_0 {(4 - 6x^{2} )} \, dx= - 74

Given that

\int\limits^1_0 {x^{2} } \, dx = 13

We find

\int\limits^1_0 {(4 - 6x^{2} )} \, dx

<h3>Definite integrals </h3>

Definite integrals are integral values that are obtained by integrating a function between two values.

So, Integral \int\limits^1_0 {(4 - 6x^{2} )} \, dx

So, \int\limits^1_0 {(4 - 6x^{2} )} \, dx = \int\limits^1_0 {4} \, dx - \int\limits^1_0 {6x^{2} } \, dx \\=  4[x]^{1}_{0}    - \int\limits^1_0 {6x^{2} } \, dx \\=  4[x]^{1}_{0}    - 6\int\limits^1_0 {x^{2} } \, dx \\= 4[1 - 0]    - 6\int\limits^1_0 {x^{2} } \, dx\\= 4[1]    - 6\int\limits^1_0 {x^{2} } \, dx\\= 4    - 6\int\limits^1_0 {x^{2} } \, dx

Since

\int\limits^1_0 {x^{2} } \, dx = 13,

Substituting this into the equation the equation, we have

\int\limits^1_0 {(4 - 6x^{2} )} \, dx = 4 - 6\int\limits^1_0 {x^{2} } \, dx\\= 4 - 6 X 13 \\= 4 - 78\\= -74

So, \int\limits^1_0 {(4 - 6x^{2} )} \, dx= - 74

Learn more about definite integrals here:

brainly.com/question/17074932

You might be interested in
Gọi S là tập các giá trị nguyên của tham số m trong khoảng (–20;20) để bất phương
Pie

Answer:

i cannot understand

Step-by-step explanation:

5 0
3 years ago
Over the weekend, statton and tyler drove to montana to go hunting. now they're preparing to go home.tyler needs gas for his jee
Shtirlitz [24]
The jeep gets 22 miles per gallon...

he has 5 gallons in the tank already....
buys gas at 1.25 per gallon.....spends $ 22...so he buys 22 / 1.25 = 17.6 gallons
so he has a total of (5 + 17.6) = 22.6 gallons....at 22 miles per gallon =
22.6 * 22 = 497.2 miles <==
7 0
3 years ago
(2+i \sqrt{2}), (2- i\sqrt{2} )
juin [17]
Idk hi what’s up with y’all and josh
7 0
3 years ago
How do I find the x and the y
mart [117]

Answer:

x = 22

y = 35

Step-by-step explanation:

Because its an isosceles triangle, you know the base angles are equal so:

3x - 11 = 2x + 11

Solving:

subtract 2x from both sides

x-11=11

add 11 to both sides

x = 22

Next, find the angle measures of the two base angles:

3*22-11\\66-11\\55

To find y, you know that the interior angles of the whole triangle add up to 180, so you have

55 + 55 + 2y = 180

solving,

110 + 2y = 180

subtract 110 from both sides

2y = 70

divide both sides by 2

y = 35

3 0
2 years ago
Read 2 more answers
The power generated by an electrical circuit (in watts) as function of its current x (in amperes) is modeled by: P(x)=-12x^2 +12
Minchanka [31]

Given:

The power generated by an electrical circuit (in watts) as function of its current x (in amperes) is modeled by:

P(x)=-12x^2+120x

To find:

The current that will produce the maximum power.

Solution:

We have,

P(x)=-12x^2+120x

Here, leading coefficient is negative. So, it is a downward parabola.

Vertex of a downward parabola is the point of maxima.

If a parabola is f(x)=ax^2+bx+c, then

Vertex=\left(\dfrac{-b}{2a},f(\dfrac{-b}{2a})\right)

In the given function, a=-12 and b=120. So,

-\dfrac{b}{2a}=-\dfrac{120}{2(-12)}

-\dfrac{b}{2a}=-\dfrac{120}{-24}

-\dfrac{b}{2a}=5

Putting x=5 in the given function, we get

P(5)=-12(5)^2+120(5)

P(5)=-12(25)+600

P(5)=-300+600

P(5)=300

Therefore, 5 watt current will produce the maximum power of 300 amperes.

6 0
3 years ago
Other questions:
  • I need help hurry plz
    8·2 answers
  • Mr. Marvi's Class is fund-raising for a field trip that costs $1254. The school is
    5·2 answers
  • If triangle VWX and triangle NOP are similar. If mV=44 degrees and mP=66 degrees. What is mW?
    14·1 answer
  • Franklin rode his bike 6 5/6 miles on Tuesday. He also rode his bike 5 5/6 miles on Thursday. What is the difference between the
    15·1 answer
  • The National Health Interview Survey, which included a questionnaire administered during in-person interviews with 21,781 adults
    10·1 answer
  • Sandy bought a 32.5 ounce package of mixed nuts for $7.I5. What was the coat per ounce.​
    13·1 answer
  • On a cold January day, Mavis noticed that the temperature dropped 21 degrees over the course of the day to 9 degrees Celcius. Wr
    14·1 answer
  • N=4/5(m+7);m literal equation
    7·1 answer
  • Given that CD is the perpendicular bisector of AB, which of the following statements can be used
    7·1 answer
  • . Trevor mows 5 times as
    8·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!