Chapter 4: Q. 35 (page 405)

The signed area between the graph of $f (x) = 3 x^{2} - 7 x + 2$ and the $x$ -axis on $[0, 4] .$

Short Answer

Expert verified

The area between the graph of $f (x)$ and $x$ is $16 .$

Step by step solution

Step 1. Given information

The given function is $f (x) = 3 x^{2} - 7 x + 2,$ we need to sign the area between the graph of $f (x)$ and the $x$ -axis on $[0, 4] .$

Step 2. Calculation

$f (x) = 3 x^{2} - 7 x + 2 .$

The sign area between the graph of $f (x)$ and the $x$ -axis on $[0, 4]$ is,

$A = \int_{0}^{4} f (x) d x .$

$= \int_{0}^{4} (3 x^{2} - 7 x + 2) d x .$

$= {[\frac{3 x^{3}}{3} - 7 (\frac{x^{2}}{2}) + 2 x]}_{0}^{4} .$

$= {(4)}^{3} - \frac{7}{2} {(4)}^{2} + 2 (4) .$

$= 64 - 56 + 8 .$

$= 16 .$

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.

The signed area between the graph of $f (x) = 3 x^{2} - 7 x + 2$ and the $x$ -axis on $[0, 4] .$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Mechanics Maths

Geometry

Applied Mathematics

Probability and Statistics

Logic and Functions

Study anywhere. Anytime. Across all devices.

The signed area between the graph of fx=3x2-7x+2and the x-axis on0,4.

Short Answer

Step by step solution

Step 1. Given information

Step 2. Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Mechanics Maths

Geometry

Applied Mathematics

Probability and Statistics

Logic and Functions

Study anywhere. Anytime. Across all devices.

The signed area between the graph of $f (x) = 3 x^{2} - 7 x + 2$ and the $x$ -axis on $[0, 4] .$