Write the Riemann sum to find the area under the graph of the function f(x) = x3 from x = 2 to x = 5.

Answers

Answer 1

Answer:

Answer: The answer is 152.25 sq units.

Step-by-step explanation: Given function to be integrated is

$f(x)=x^3,~~x=2~~\textup{to}~~x=5.$

To find the area of the given curve from x = 2 to 5, first we need to integrate the function and we will put the boundary values and subtract the smallest from largest value.

The Riemann sum and the formula to find the area is given by

$A=\int_(x=2)^(5)f(x)dx\n\n\Rightarrow A=\int_(2)^(5)x^3dx\n\n\Rightarrow A=[(x^4)/(4)]_2^5=(1)/(4)(625-16)=152.25$

Thus, the required area is 152.25 sq units.

Answer 2

Answer:

The area under the graph of the function $f\left( x \right) = {x^3}$ from $x = 2$ to $x = 5$ is $\boxed{152.25{\text{ unit}}{{\text{s}}^2}}.$

Further explanation:

Given:

The function is $f\left( x \right) = {x^3}.$

The function is defined in the interval from $x = 2$ to $x = 5.$

Explanation:

The given function is $f\left( x \right) = {x^3}.$

Integrate the given function with respect x.

$\begin{aligned}Area &= \int\limits_2^5 {f\left( x \right)dx} \n&= \int\limits_2^5 {{x^3}dx}\n&= \left[ {\frac{{{x^4}}}{4}} \right]_2^5\n&= \left( {\frac{{{5^4}}}{4} - \frac{{{2^4}}}{4}} \right)\n\end{aligned}$

Further solve the above equation to obtain the area under the curve,

$\begin{aligned}{\text{Area}} &= \frac{{625}}{4} - \frac{{16}}{4}\n&= \frac{{625 - 16}}{4}\n&= 152.25\n\end{aligned}\n$

The area under the graph of the function $f\left( x \right) = {x^3}$ from $x = 2$ to $x = 5$ is $\boxed{152.25{\text{ unit}}{{\text{s}}^2}}.$

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Answer details:

Grade: High school

Subject: Mathematics

Chapter: Riemann function

Keywords: Riemann, sum, area, graph function, Riemann sum, area under the curve, function, $f(x) -= x3, x = 2, x = 5.$

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Find all real zeros of the function.
f(x)=4(x^2-1)(x-3)(x+3)^2

Answers

4(x^2 - 1)(x - 3)(x + 3)^2 = 0
(x + 1)(x - 1)(x - 3)(x + 3) = 0
x = -1, 1, 3, -3

Given: 2x + 3y = 6. What is the y-intercept?

Answers

Substituting x=0 , we get
2*0+3y = 6
3y=6
y=2 is the y intercept.

Final answer:

To find the y-intercept in an equation, we set x equal to 0 and solve for y. For the equation 2x + 3y = 6, when x is replaced with 0, it simplifies to 3y = 6. Dividing by 3 gives y = 2, meaning the y-intercept of the line is 2.

Explanation:

The given equation in this question is in the standard form of a linear equation which can be represented in slope-intercept form of y = mx + b, where m is the slope and b is the y-intercept. To find the y-intercept, we'll want to set x equal to 0 and solve for y.

So in this equation of 2x + 3y = 6, we'll set x to 0. That leaves us with 3y = 6. Solve for y by dividing by 3 on both sides. This gives us y = 2, which is the y-intercept.

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The area of a square piece of land in square units can be represented by the expression 9q4r8s6. What is the length of one side of the piece of land?

Answers

The length of one side of the piece of land is $41.6√(qrs)$ .

What is area?

The space occupied by a flat shape or the surface of an object is called area.

Formula for the area of a square

$A = x^(2)$

Where,

A is the area of square

x is length of side of the square

According to the given question

Expression for the area of a square = 9q4r8s6 = 1728qrs

Let the length of the side of square be x unit.

Area of square = $x^(2)$

⇒ 1728qrs = $x^(2)$

⇒ $x = √(1728qrs)$

⇒ $x = 41.6√(qrs)$

Therefore, the length of one side of the piece of land is $41.6√(qrs)$ .

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Answer:

The answer is: 3q^2r^4|s^3| units!

Step-by-step explanation:

Just took the quiz, and this was the answer. Hope it helps! :)

8- 4 1/2 a 31/2 b 3 c4 d 41/2

Answers

8 - 4 1/2 =
8 - 9/2 =
16/2 - 9/2 =
7/2 =
3 1/2

Question 1 (1 point)Find the coordinates of point P that divides the directed line segment from A to B in the given ratio. A(1, 2), B(5, 4), 1 to 1

Answers

Answer:

P ( -1, -3)

Step-by-step explanation:

Given ratio is AP : PB = 3 : 2 = m : n and points A(5,6) B(-5,-9)

We will calculate coordinates of the point P which divides line segment AB in the following way:

xp = (n · xa + m · xb) / (m+n) = (2 · 5 + 3 · (-5)) / (3+2) = (10-15) / 5 = -5/5 = -1

xp = -1

yp = (n · ya + m · yb) / (m+n) = (2 · 6 + 3 · (-9)) / (3+2) = (12-27) / 5 = -15/5 = -3

yp = -3

Point P( -1, -3)

PLEASEEEEEEEEEEEEEEEEEE URGENT

Answers

Option C:

f(x) = 5x + 7 is the function of the input-output table.

Solution:

Option A: f(x) = 6x + 9

Input x = 1 in the above equation.

f(1) = 6(1) + 9

= 6 + 9

f(1) = 15

But the output is 12 in the table.

So, it is not the function of the table.

Option B: f(x) = 7x + 5

Input x = 1 in the above equation.

f(1) = 7(1) + 5

f(1) = 12

Input x = 5 in the above equation.

f(5) = 7(5) + 5

f(5) = 40

But the output is 32 in the table.

So, it is not the function of the table.

Option C: f(x) = 5x + 7

Input x = 1 in the above equation.

f(1) = 5(1) + 7

f(1) = 12

Input x = 5 in the above equation.

f(5) = 5(5) + 7

f(5) = 32

Input x = 10 in the above equation.

f(10) = 5(10) + 7

f(10) = 57

Input x = 5 in the above equation.

f(15) = 5(15) + 7

f(15) = 82

All outputs are correct for the given input.

Hence it is the function of the table.

Option D: f(x) = 12x + 1

Input x = 1 in the above equation.

f(1) = 12(1) + 1

f(1) = 12

Input x = 5 in the above equation.

f(5) = 12(5) + 1

f(5) = 61

But the output is 32 in the table.

So, it is not the function of the table.

Hence Option C is the correct answer.

f(x) = 5x + 7 is the function of the input-output table.

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