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Sonbull [250]
3 years ago
10

Find the most general antiderivative of the function. (Check your answer by differentiation. Use C for the constant of the antid

erivative. Remember to use absolute values where appropriate.) f(x) = 2 5 − 3 x , x > 0
Mathematics
1 answer:
storchak [24]3 years ago
8 0

Answer:

C + ⅖|x| - (³/₂)x²

Step-by-step explanation:

ƒ(x) = ⅖ - 3x ; x > 0

The antiderivative of ƒ(x) is a function that you can differentiate to get ƒ(x). It is the indefinite integral of ƒ(x).

Thus, if ƒ(x) = ⅖ - 3x, we must find ∫(⅖ - 3x)dx .

∫(⅖ - 3x)dx = ∫⅖dx - ∫3xdx = ⅖∫dx - 3∫xdx

(a) Integrate the first term

⅖∫dx = ⅖x

(b) Integrate the second term

∫xdx =½x², so

3∫xdx = (³/₂)x²

(c) Add the constant of integration, C

Remember that dC/dx =0 when C is a constant.

We don't know if there's a constant term in the antiderivative (there may or may not be one), so we include the constant term C to make it general.

(d) Combine the three terms

∫(⅖ - 3x)dx = C + ⅖x - (³/₂)x²

We must have x  > 0, so

∫ƒ(x)dx = C + ⅖|x| - (³/₂)x²

Check:

(d/dx)( C + ⅖|x| - (³/₂)x²) = 0 + ⅖ - 3x  = ⅖ - 3x

Differentiating the integral returns the original function.

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Step-by-step explanation:

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3 years ago
Read 2 more answers
F(x) = 2x is translated 4 units up
kolbaska11 [484]

 

f(x) = 2x

f(x) = 2x + 4   (Is translated 4 units up.)

6 0
3 years ago
How to solve using substitution
DiKsa [7]
X+5 = x^2 - x + 2
0 = x^2 -2x - 3
0 = (x-3)(x+1)

x = -1,3

y = -1 + 5 OR y = 3+5
y = 4 OR y = 8

y = 4,8

So we have two ordered pairs, (-1,4) and (3,8).

Hope that helped!

can you mark my answer as brainliest btw?

4 0
3 years ago
A small motorboat travels 12mph in still water. It takes 2 hours longer to travel 46 miles going upstream than it does going dow
Natasha_Volkova [10]

Using the relation between velocity, distance and time, it is found that the rate of the current is of 3.33 mph.

<h3>What is the relation between velocity, distance and time?</h3>

Velocity is distance divided by time, hence:

v = d/t

A small motorboat travels 12mph in still water. With the current, upstream, 46 miles are traveled in t hours, hence:

12 + r = 46/t

r = 46/t - 12

Downstream, the time is of t + 2 hours, hence:

12 - r = 46/(t + 2)

r = 12 - 46/(t + 2)

Hence, equaling the values for r:

46/t - 12 = 12 - 46/(t + 2)

46/t + 46/(t + 2) = 24

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92t + 92 = 24t² + 48t

24t² - 44t - 92 = 0

Using a quadratic equation calculator, the solution is t = 3. Hence the rate is found as follows:

r = 46/t - 12 = 46/3 - 12 = 3.33 mph.

More can be learned about the relation between velocity, distance and time at brainly.com/question/28155966

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What is the force, in N, when a pressure of 18 N/m2 is exerted on an area of 500 cm2?
zalisa [80]

Answer:  1.6 N/cm^2

Step-by-step explanation:

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