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krok68 [10]
2 years ago
6

Find the general indefinite integral. (use c for the constant of integration. )

Mathematics
1 answer:
Vlada [557]2 years ago
7 0

The indefinite integral will be  \int (7x^2+8x-2)dx=\dfrac{7x^3}{3}+4x^2-2x+C)

<h3 /><h3>what is indefinite integral?</h3>

When we integrate any function without the limits then it will be an indefinite integral.

General Formulas and Concepts:

Integration Rule [Reverse Power Rule]:                                                              

\int x^ndx=\dfrac{x^{n+1}}{n+1}}+C

Integration Property [Multiplied Constant]:                                                        

\int cf(x)dx=c\int f(x)dx

Integration Property [Addition/Subtraction]:                                                      

\int [f(x)\pmg(x)]dx=\int f(x)dx\pm \intg(x)dx

[Integral] Rewrite [Integration Property - Addition/Subtraction]:

\int (7x^2+8x-2)dx=\int 7x^2dx+\int 8xdx    -\int 2dx          

[Integrals] Rewrite [Integration Property - Multiplied Constant]:  

\int (7x^2+8x-2)dx=7 \int x^2dx+ 8 \int xdx    -2\int dx            

[Integrals] Reverse Power Rule:    

\int (7x^2+8x-2)dx= 7(\dfrac{x^3}{3})+8(\dfrac{x^2}{2})-2x+C                                                            

Simplify:    

\int (7x^2+8x-2)dx= \dfrac{7x^3}{3}+4x^2-2x+C                                                                                                      

So the indefinite integral will be \int (7x^2+8x-2)dx= \dfrac{7x^3}{3}+4x^2-2x+C                

To know more about indefinite integral follow

brainly.com/question/27419605

#SPJ4

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Given c=(2.4,0.45) and d = (7,-4) find the direction of 5c+4d
kakasveta [241]

Answer:

The direction of 5c + 4d is approximately 19.0° clockwise with

the positive part of x-axis

Step-by-step explanation:

* Lets talk about the direction of a vector

- If the vector is (x , y), then  

# Its magnitude is √(x² + y²)

# Its direction is tan^-1 (y/x)

- The direction is the angle between the positive part of x-axis and  

  the vector

* Lets solve the problem

∵ c = (2.4 , 0.45) and d = (7 , -4)

- To find 5c + 4d , multiply the two coordinates of c by 5 and the two

  coordinates of d by 4

# Multiply c by 5

∴ 5c = [5(2.4) , 5(0.45)]

∴ 5c = (12 , 2.25)

# Multiply d by 4

∴ 4d = [4(7) , 4(-4)]

∴ 4d = (28 , -16)

- Lets add 5c and 4d

∴ 5c + 4d = (12 , 2.25) + (28 , -16)  

∴ 5c + 4d = [(12 + 28) , (2.25 + -16)]

∴ 5c + 4d = (40 , -13.75)

- The vector is in the 4th quadrant because the x-coordinate is

 positive and the y-coordinate is negative

* Find the direction of 5c + 4d

∵ The direction is tan^-1 (y/x)

∴ The direction is tan^-1 (-13.75/40) = -18.97°

* The direction of 5c + 4d is approximately 19.0° clockwise with

 the positive part of x-axis

3 0
3 years ago
PLEASE HELP DUE TODAY!!
telo118 [61]

9514 1404 393

Answer:

  2.8¢, true

Step-by-step explanation:

The value of copper in a penny is reportedly about ...

  (0.95 × 3.11 g)×(1 oz)/(28.35 g)×($0.27/oz) ≈ $0.028

Today, the value of the copper in a pre-1982 penny is about 2.8¢, more than double the value of the penny as legal tender.

The claim is true.

7 0
2 years ago
Harold bought 3 pounds of red apples and 4.2 pounds of green apples from a grocery store, where both kinds of apples are $1.75 a
Lelechka [254]
The answer is 11.6
add 3+4.2= 7.2 times 1.75
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2 years ago
PLEASE HELP !! BRAINLIEST AND 10 POINTS
Bumek [7]
POINT A I had the same question in my math class !!!
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3 years ago
Katie is twice as old as her sister Mara. The sum of their ages is 24. Find their ages.
Alenkasestr [34]
So k=katie's' age
m=mara's age

k is 2 times as old as m
k=2m

sum is 24
add means sum
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so we have
k+m=24 and
k=2m
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2m+m=24
add
3m=24
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4 0
3 years ago
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