3. | (1- 2x) dx 0.

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question
In the following exercises, given that

\[
\int_0^1 x \, dx = \frac{1}{2}, \quad \int_0^1 x^2 \, dx = \frac{1}{3}, \quad \text{and} \quad \int_0^1 x^3 \, dx = \frac{1}{4},
\]

compute the integrals.
Transcribed Image Text:In the following exercises, given that \[ \int_0^1 x \, dx = \frac{1}{2}, \quad \int_0^1 x^2 \, dx = \frac{1}{3}, \quad \text{and} \quad \int_0^1 x^3 \, dx = \frac{1}{4}, \] compute the integrals.
The image shows a mathematical integral expression. The integral is set up as follows:

\[
\int_{0}^{1} (1 - 2x)^3 \, dx
\]

This expression represents the definite integral of the function \((1 - 2x)^3\) with respect to \(x\), evaluated from the lower limit of 0 to the upper limit of 1. Such integrals are often used in calculus to find the area under a curve between two points, or to solve problems involving accumulation and rates of change.
Transcribed Image Text:The image shows a mathematical integral expression. The integral is set up as follows: \[ \int_{0}^{1} (1 - 2x)^3 \, dx \] This expression represents the definite integral of the function \((1 - 2x)^3\) with respect to \(x\), evaluated from the lower limit of 0 to the upper limit of 1. Such integrals are often used in calculus to find the area under a curve between two points, or to solve problems involving accumulation and rates of change.
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