Chapter 4: Q. 3 (page 372)

Approximating with a Riemann sum:
Use a right sum with $10$ rectangles to approximate the area under the graph of $f (x) = x^{2}$ on [0, 5].

Short Answer

Expert verified

The area of the area under the graph $f (x) = x^{2}$ on the interval $[0, 5]$ is $48.125$ .

Step by step solution

Step 1. Given Information.

The function:

$f (x) = x^{2} o n [0, 5]$

Step 2. Graph the function on the graph.

Sketch the graph.

Step 3. Find the area.

The area is divided into $10$ rectangles. so, each rectangle is of length $∆ x = 0.5$ .

Area, $A = f (0.5) ∆ x + f (1) ∆ x + f (1.5) ∆ x + f (2) ∆ x + f (2.5) ∆ x + f (3) ∆ x + f (3.5) ∆ x + f (4) ∆ x + f (4.5) ∆ x + f (5) ∆ x = 0.25 (0.5) + 1 (0.5) + 2.25 (0.5) + 4 (0.5) + 6.25 (0.5) + 9 (0.5) + 12.25 (0.5) + 16 (0.5) + 20.25 (0.5) + 25 (0.5) = 48.125$

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Approximating with a Riemann sum:
Use a right sum with $10$ rectangles to approximate the area under the graph of $f (x) = x^{2}$ on [0, 5].

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Graph the function on the graph.

Step 3. Find the area.

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Approximating with a Riemann sum:Use a right sum with 10 rectangles to approximate the area under the graph of f(x)=x2 on [0, 5].

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Graph the function on the graph.

Step 3. Find the area.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Calculus

Mechanics Maths

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Study anywhere. Anytime. Across all devices.

Approximating with a Riemann sum:
Use a right sum with $10$ rectangles to approximate the area under the graph of $f (x) = x^{2}$ on [0, 5].