교과서 질문
2. When applying the formula for integration by parts, how do you choose the u and dv? How can you apply integration by parts to an integral of the form ∫ f(x) dx?
23
views
Ch. 8 - Techniques of Integration
Hass15th EditionThomas' CalculusISBN: 9780137616077
당신이 사용하는 게 아니라요?교과서 변경다른 교과서를 선택하세요
TOC.tableOfContents
- Ch. 1 - Functions155
- Ch. 2 - Limits and Continuity240
- Ch. 3 - Derivatives337
- Ch. 4 - Applications of Derivatives293
- Ch. 5 - Integrals41
- Ch. 6 - Applications of Definite Integrals25
- Ch. 7 - Transcendental Functions490
- Ch. 8 - Techniques of Integration399
- Ch. 9 - First-Order Differential Equations66
- Ch. 10 - Infinite Sequences and Series132
- Ch. 11 - Parametric Equations and Polar Coordinates58
8장, 문제 8.GYR.7
7. What is the goal of the method of partial fractions?
검증된 단계별 안내1
Understand that the method of partial fractions is used to decompose a complex rational function into a sum of simpler rational expressions whose denominators are factors of the original denominator.
Recognize that this decomposition makes it easier to perform operations such as integration or inverse Laplace transforms on the original rational function.
Identify the denominator of the given rational function and factor it completely into linear and/or irreducible quadratic factors.
Express the original rational function as a sum of fractions, each with one of the factors in the denominator and unknown constants in the numerators.
Solve for the unknown constants by multiplying both sides by the common denominator and equating coefficients or substituting convenient values of the variable.
비슷한 문제에 대한 검증된 영상 답변:
이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.
영상 길이:
1m도움이 되었나요?
주요 개념
질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.
Partial Fraction Decomposition
Partial fraction decomposition is a technique used to express a complex rational function as a sum of simpler fractions. This simplification makes integration and other operations easier by breaking down complicated expressions into manageable parts.
추천 영상:
가이드 코스
10:07
Partial Fraction Decomposition: Distinct Linear Factors
Rational Functions
A rational function is a ratio of two polynomials. Understanding the structure of rational functions is essential because partial fractions apply specifically to these types of functions, allowing us to rewrite them in simpler forms.
추천 영상:
6:04Intro to Rational Functions
Integration of Rational Functions
One primary goal of partial fractions is to facilitate the integration of rational functions. By decomposing a complex fraction into simpler terms, each term can be integrated using basic integral formulas, making the overall integration process more straightforward.
추천 영상:
6:04Intro to Rational Functions
관련 실천
교과서 질문
Evaluate the integrals in Exercises 69–134. The integrals are listed in random order so you need to decide which integration technique to use.
∫ (sin5t) dt / [1 + (cos5t)²]
10
views
교과서 질문
Finding arc length
Find the length of the curve
y = ∫ from 0 to x of √(cos(2t)) dt, 0 ≤ x ≤ π/4.
42
views
교과서 질문
Evaluate the integrals in Exercises 69–134. The integrals are listed in random order so you need to decide which integration technique to use.
123. ∫ √x * √(1 + √x) dx
41
views
교과서 질문
Evaluate the integrals in Exercises 69–134. The integrals are listed in random order so you need to decide which integration technique to use.
∫ dy / (y² − 2y + 2)
17
views
교과서 질문
Use the substitutions in Equations (1)–(4) to evaluate the integrals in Exercises 33–40. Integrals like these arise in calculating the average angular velocity of the output shaft of a universal joint when the input and output shafts are not aligned.
∫(from π/2 to 2π/3) cos θ dθ / (sin θ cos θ + sin θ)
36
views