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Chapter 5: Q.0 (page 416)

Read the section and make your own summary of the material.

Short Answer

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The summary of the exercise.

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01

Introduction

The summary of the section about Algebra, Differentiation, Integration and expressing geometric interpretation into integration.

02

Explanation

Algebra: All the variables or functions consider under algebra. Any expression or equation is written in algebraic form. There are some formulas and identities to simplify the expression.

Differentiation: it is a process to find the instantaneous rate of change in function based on one of its variables. Reduce the whole function into small parts.

Integration or Antiderivative:It is adding or summarizing a small part of a function into a whole or complete function. It is the opposite process of differentiation.

Geometric Representation into Integration: In this process find the area of the geometry figure using integration. By adding a small part area to the complete area.

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Most popular questions from this chapter

Explain why, if x=asinu, then a2鈭�x2=acosu. Your explanation should include a discussion of domains and absolute values.

Explain why 鈭�2xx2+1dxand 鈭�1xlnxdxare essentially the same integral after a change of variables.

Explain how to know when to use the trigonometric substitutions x=asin鈦�u,x=atan鈦�u,andx=asec鈦�u, Describe the trigonometric identity and the triangle that will be needed in each case. What are the possible values for xand uin each case?

Suppose u(x)=x2. Calculate and compare the values of the following definite integrals:

role="math" localid="1648786835678" 鈭�-15u2du,鈭�x=-1x=5u2duand鈭�u(-1)u(5)u2du

Solve each of the integrals in Exercises 39鈥�74. Some integrals require trigonometric substitution, and some do not. Write your answers as algebraic functions whenever possible.

鈭�13-x2dx
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