Chapter 4: Q. 8 (page 404)

Riemann sums: Calculate each of the following Riemann sum
approximations for the definite integral of f on [a, b], using the
given value of n.
The right sum for $f (x) = \sqrt{x}$ on $[0, 4], n = 8$

Short Answer

Expert verified

The right sum is $3 \cdot 17302$ .

Step by step solution

Step 1. Given information .

Consider the given function $f (x) = \sqrt{x}$ .

Step 2. Formula used .

The formula for right sum is $S = \sum_{i = 1}^{n} δ x \cdot f (x_{i})$ .

Step 3. Find the right sum .

$f (x) = \sqrt{x}, [0, 4] δ x = \frac{4 - 0}{n} = \frac{4}{n} S = {\sum δ x \cdot f (x_{i})}_{i = 1}^{8} = δ x \cdot f (0 \cdot 5) + δ x \cdot f (1) + δ x \cdot f (1 \cdot 5) + δ x \cdot f (2) + δ x \cdot f (2 \cdot 5) + δ x \cdot f (3) + δ x \cdot f (3 \cdot 5) + δ x \cdot f (4) = 0 \cdot 5 \times \sqrt{0 \cdot 5} + 0 \cdot 5 \times \sqrt{1} + 0 \cdot 5 \times \sqrt{1 \cdot 5} + 0 \cdot 5 \times \sqrt{2} + 0 \cdot 5 \times \sqrt{2 \cdot 5} + 0 \cdot 5 \times 2 = 3 \cdot 17302$

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Riemann sums: Calculate each of the following Riemann sum
approximations for the definite integral of f on [a, b], using the
given value of n.
The right sum for $f (x) = \sqrt{x}$ on $[0, 4], n = 8$

Short Answer

Step by step solution

Step 1. Given information .

Step 2. Formula used .

Step 3. Find the right sum .

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Riemann sums: Calculate each of the following Riemann sumapproximations for the definite integral of f on [a, b], using thegiven value of n.The right sum forfx=xon0,4,n=8

Short Answer

Step by step solution

Step 1. Given information .

Step 2. Formula used .

Step 3. Find the right sum .

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Decision Maths

Pure Maths

Logic and Functions

Applied Mathematics

Geometry

Study anywhere. Anytime. Across all devices.

Riemann sums: Calculate each of the following Riemann sum
approximations for the definite integral of f on [a, b], using the
given value of n.
The right sum for $f (x) = \sqrt{x}$ on $[0, 4], n = 8$