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      • :: Worked Out Problems XIII
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QUESTION :  " How do you solve Indefinite Integrals using U-Substitution? "
Substitution is a hugely powerful technique in integration.

​Though the steps are similar for definite and indefinite integrals, there are two differences, and many of us have trouble keeping them straight. 

This page sorts them out in a convenient table, followed by a side-by-side example : to the right:
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  • The disciplines that utilize calculus include physics, engineering, economics, statistics, and medicine.

  • Used to create mathematical models in order to arrive into an optimal solution.

  • In Physics concepts of calculus include motion, electricity, heat, light, harmonics, acoustics, astronomy, and dynamics. In fact, even advanced physics concepts including electromagnetism and Einstein's theory of relativity use calculus.

  • In chemistry, calculus can be used to predict functions such as reaction rates and radioactive decay. In biology, it is utilized to formulate rates such as birth and death rates, model biological research, the use of process calculi to represent biological systems has led to the design of different calculi such as brane calculi and κ-calculus. Both have proved to be useful to model different types of biological systems.
    ​

  • In economics, calculus is used to compute marginal cost and marginal revenue, enabling economists to predict maximum profit in a specific setting.
  • In addition, it is used to check answers for different mathematical disciplines such as statistics, analytical geometry, and algebra.
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  • Ask
  • FAQ
  • R Winter Series
    • Create & Manipulate Matrices
    • Data Cleaning, Data Frames & Lists
    • Tidyverse
    • Creating Graphs with ggplot
  • AP CS A
    • Java July Series >
      • :: Classes & OOPs
      • :: Interface
      • :: Inheritance
      • :: Intro To Arrays Java
      • :: Arrays Continued
    • :: CS-A or CS-P?
    • :: Control Structures
    • :: Recursion
    • :: While Do While Loops in Java
    • :: Interface in Java
    • :: ArrayLists
    • :: Java Naming Conventions
    • :: Logic Circuits
    • :: Getters and Setters
    • :: Binary & Hexadecimal
  • Summer 2020 Tutoring
    • :: REPRESENT IT!
    • Pre-Algebra Sessions >
      • :: Basic Division
      • :: Complex Division
      • :: Estimation Division
      • :: Division Practice Problems
    • Algebra II >
      • :: Cubic Equations
      • :: Complex Numbers
    • Chemistry >
      • Molarity Basics
    • C++ Sessions >
      • :: Introduction
      • :: Style v Syntax
      • :: Variables & Data Types
      • :: Intialize/Declare Variables
      • :: Types of Operators
      • :: Strings and Input - Output
      • :: How to Construct Arrays
  • AP Bio
    • :: Sketch Notes >
      • :: Part 1
      • :: Part 2
    • :: epigenetics
    • :: Chi-Squared Tests
    • :: Cancer
    • :: Hox Genes
    • :: Hardy-Weinberg Principle
    • :: Rule of Multiplication + Addition for Punnett Squares
    • :: CRISPR
    • :: Amino Acid
    • :: Peptide
    • :: Why study Peptides
    • :: Aquaporins
    • :: Gram Stains
    • :: Graph on Excel for Bio Lab
  • AP Chem
    • Organic Chemistry
    • I. Properties of Matter >
      • Neutralization
    • II. Periodic table >
      • Org of Periodic Table
      • :: Groups
    • III. Chemical bonding >
      • :: Mass to Mass conversion
      • :: Naming Acids
      • :: Cross Drop Charge
      • :: Predicting Products
      • :: Balance Equation Question
      • :: Learn to Balance Equation
      • :: VSEPR Simulation
    • IV. Molar Mass >
      • ::LR ER and excess reatant
      • :: Molecular/Formula Mass
      • :: Empirical Formula & Molar Mass
      • :: Percentages & Empirical Formula
      • :: Empirical formula
    • IV. Solutions and Solubility >
      • :: Types of Solutions with Solubility Curves
      • :: Solubility Curve
    • V. Easy Tricks and Tips >
      • :: Tip to Molecular Shapes
      • Memorizing Bond Angles and Polarity
      • :: Chemistry Formulas
      • :: Trick Polyatomic ions
    • VI. General AP Concepts >
      • :: Potential Energy Diagrams
      • :: Haber-Bosch
      • :: Le Chatelier
      • :: Pressure & Moles
      • ::Rydberg's Constant vs Unit of Energy
      • :: Equilibrium and RICE Tables
      • :: Kinetics
      • Galvanic Cells
    • :: Flash cards
    • :: VSEPR
  • AP Stats
    • Chi-Squared Tests
    • Solving Chi-Sqd Test Using Sheets
    • Applications of Statistics
    • Standardized Scores
    • Distributions Transformations
  • AP Calc
    • DI Method - Tabular Integration
    • Polar Curves: Tangent Line and Slope
    • Riemann Sums: Left and Right Approximations
    • :: Conic Sections Flash cards
    • :: Parent Functions Flash cards
    • Worked Out Problems >
      • :: Worked Out Problems I
      • :: Worked Out Problems II
      • :: Worked Out Problems III
      • :: Worked Out Problems IV
      • :: Worked Out Problems V
      • :: Worked Out Problems VI
      • :: Worked Out Problems VII
      • :: Worked Out Problems VIII
      • :: Worked Out Problems IX
      • :: Worked Out Problems X
      • :: Worked Out Problems XI
      • :: Worked Out Problems XII
      • :: Worked Out Problems XIII
    • Applying Trig Identities
    • L'Hopital's Rule
    • Differences Between Conic Sections
    • Graphing Conic Sections
    • :: Pre-Calc - Trig Identities
    • Tangent & Normal Lines
    • Indefinite integrals: U Sub
    • Calculus Derivatives >
      • Product Rule
      • Quotient Rule
      • Chain Rule
  • Arduino
    • Quick Look
    • Project #1: Blinking LED
    • Project #2: Button LED
    • Project #3: Flowing LED
    • Project #4: LCD Display
    • Project #5: Serial Monitor
  • AP Español
    • AP Español Salsa
  • App
    • AP Go Pow How?
    • AP Go Pow APP Page
  • Musings
    • :: Bayesian Example
    • :: Nash equilibria
    • :: Bayesian Nash Equilibrium
    • :: Backward induction
    • :: what is ISS
    • :: Rotational Matrices
    • :: Primary v Secondary Pollutants
    • :: Black Hole
    • :: Covid-19 Hackathon
    • :: Evolution of Immunizations
    • :: Predictions of Diseases
    • :: Book List
    • :: Patterncount
    • :: Binary Classification
    • :: Cybersecurity
    • :: What is CIA Triad
    • :: What is Networking
    • :: Self Similarity
    • :: Trig Identities
    • :: UIL Number S
    • :: Box Offensive Play
    • :: Why Card Trick Works
    • :: Easy Multiplication
  • AP CREDIT
  • About