Chapter 4: Q. 5 (page 351)

Fill in the blanks: The definite integral of an integrable function f from $x = a t o x = b$ is defined to be
where $∆ x =_____, x_{k =}________& x_{k}^{*} =________$

Short Answer

Expert verified

The blanks are $Δ x = \frac{b - a}{n}, x_{k} = a + k Δ x & x_{k}^{*} = x_{k}$

Step by step solution

Step 1. Given information

Fill in the blanks given as $∆ x =_____, x_{k =}________& x_{k}^{*} =________$

Step 2. Fill the blanks

The definite integral can be written as

$\int_{a}^{b} f (x) d x = \lim_{n \to \infty} \sum_{k = 1}^{n} f (x_{k}^{*}) Δ x$

Therefore, $Δ x = \frac{b - a}{n}, x_{k} = a + k Δ x & x_{k}^{*} = x_{k}$

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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Fill in the blanks: The definite integral of an integrable function f from $x = a t o x = b$ is defined to be
where $∆ x =_____, x_{k =}________& x_{k}^{*} =________$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Fill the blanks

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Calculus

Probability and Statistics

Pure Maths

Applied Mathematics

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Fill in the blanks: The definite integral of an integrable function f from x=atox=bis defined to bewhere∆x=_____,xk=________&xk*=________

Short Answer

Step by step solution

Step 1. Given information

Step 2. Fill the blanks

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Calculus

Probability and Statistics

Pure Maths

Applied Mathematics

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Fill in the blanks: The definite integral of an integrable function f from $x = a t o x = b$ is defined to be
where $∆ x =_____, x_{k =}________& x_{k}^{*} =________$