Q. 34 For聽given聽function聽f聽and聽in... [FREE SOLUTION]

91影视

Chapter 4: Q. 34 (page 340)

$For given function f and interval [a, b], it is possible to find the exact signed area between the graph of f and the x - axis on [a, b] geometrically . Find this exact area, and then calculate the left, right and trapezoid sums with n = 4 . f (x) = 5, [a, b] = [- 2, 2]$

Short Answer

Expert verified

left-sum = 20, right-sum= 20 , trapezoid sum = 20.

Step by step solution

Step 1. Given Information

$The function is f (x) = 5 and the interval is [a, b] = [- 2, 2] .$

Step 2. Finding area.

The value of n = 4

Calculate the exact area using calculator

Press Math and Select 9.

Step 3. Calculating Exact Sum

$Enter the function (5, X, - 2, 2) Press ENTER The display is shown below,$

Therefore ,the exact sum is $20$

Step 4. Calculating left-sum

$The left - sum defined for n rectangles on [a, b] is {鈭�}_{k = 1}^{n} f (x_{k - 1}) 鈭� x . Where, 鈭� x = \frac{b - a}{n}, x_{k} = a + k 鈭� x . Now, 鈭� x = \frac{2 + 2}{4} = 1 . So, x_{k} = - 2 + k (1) = k - 2 . In the left sum, x_{k - 1}, is the leftmost point in the interval [x_{k - 1,} x_{k}] . So, x_{k - 1} = k - 3 . The left sum is, {鈭�}_{k = 1}^{4} 5 (1) = 5 + 5 + 5 + 5 = 20 Therefore, the left sum is 20 .$

Step 5. Calculating the right-sum

$The right - sum defined for n rectangles on [a, b] is {鈭�}_{k = 1}^{n} f (x_{k}) 鈭� x . Where, 鈭� x = \frac{b - a}{n}, x_{k} = a + k 鈭� x . Now, 鈭� x = \frac{2 + 2}{4} = 1 . So, x_{k} = - 2 + k (1) = k - 2 . The right sum is, {鈭�}_{k = 1}^{4} 5 (1) = 5 + 5 + 5 + 5 = 20 Therefore, the right sum is 20 .$

Step 6. calculating trapezoid sum

$The trapezoid sum is \frac{20 + 20}{2} = 20 Therefore, the trapezoid sum is 20 .$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

$For given function f and interval [a, b], it is possible to find the exact signed area between the graph of f and the x - axis on [a, b] geometrically . Find this exact area, and then calculate the left, right and trapezoid sums with n = 4 . f (x) = 5, [a, b] = [- 2, 2]$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Finding area.

Step 3. Calculating Exact Sum

Step 4. Calculating left-sum

Step 5. Calculating the right-sum

Step 6. calculating trapezoid sum

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Probability and Statistics

Geometry

Decision Maths

Pure Maths

Mechanics Maths

Study anywhere. Anytime. Across all devices.

91影视

Forgivenfunctionfandinterval[a,b],itispossibletofindtheexactsignedareabetweenthegraphoffandthex-axison[a,b]geometrically.Findthisexactarea,andthencalculatetheleft,rightandtrapezoidsumswithn=4.f(x)=5,a,b=-2,2

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Finding area.

Step 3. Calculating Exact Sum

Step 4. Calculating left-sum

Step 5. Calculating the right-sum

Step 6. calculating trapezoid sum

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Probability and Statistics

Geometry

Decision Maths

Pure Maths

Mechanics Maths

Study anywhere. Anytime. Across all devices.

$For given function f and interval [a, b], it is possible to find the exact signed area between the graph of f and the x - axis on [a, b] geometrically . Find this exact area, and then calculate the left, right and trapezoid sums with n = 4 . f (x) = 5, [a, b] = [- 2, 2]$