The General Power Formula

Slides:



Advertisements
Similar presentations
8.2 Integration By Parts.
Advertisements

5044 Integration by Parts AP Calculus. Integration by Parts Product Rules for Integration : A. Is it a function times its derivative; u-du B. Is it a.
Lesson 7-2 Hard Trig Integrals. Strategies for Hard Trig Integrals ExpressionSubstitutionTrig Identity sin n x or cos n x, n is odd Keep one sin x or.
More Trigonometric Integrals Lesson Recall Basic Identities Pythagorean Identities Half-Angle Formulas These will be used to integrate powers of.
Integration By Parts (c) 2014 joan s kessler distancemath.com 1 1.
CHAPTER Continuity Integration by Parts The formula for integration by parts  f (x) g’(x) dx = f (x) g(x) -  g(x) f’(x) dx. Substitution Rule that.
5.4 Exponential Functions: Differentiation and Integration The inverse of f(x) = ln x is f -1 = e x. Therefore, ln (e x ) = x and e ln x = x Solve for.
Basic Logarithmic and Exponential Integrals Lesson 9.2.
5.7 Inverse Trigonometric Functions: Integration and Completing the Square.
Integrals Related to Inverse Trig, Inverse Hyperbolic Functions
Aim: Integrate Inverse Trig Functions Course: Calculus Do Now: Aim: How do we integrate Inverse Trig functions? Complete the square, express as the sum.
Inverse Trigonometric Functions: Integration
The General Power Formula Lesson Power Formula … Other Views.
Integration by Substitution
8.2 Integration by Parts.
x x e x & ln x Inverse Trig Trig
The Natural Log Function: Integration Lesson 5.7.
Integrals of the Form: Chapter 7.3 March 27, 2007.
Integration by Parts If u and v are functions of x and have
7.2 Trigonometric Integrals Tues Jan 12 Do Now Evaluate.
Trigonometric Integrals Lesson 8.3. Recall Basic Identities Pythagorean Identities Half-Angle Formulas These will be used to integrate powers of sin and.
Lesson 3-6 Implicit Differentiation. Objectives Use implicit differentiation to solve for dy/dx in given equations Use inverse trig rules to find the.
Logarithmic, Exponential, and Other Transcendental Functions
Derivatives of Inverse Trigonometric Functions. Integrals.
2.8 Integration of Trigonometric Functions
Warm-Up Find the derivative.
Section 8.3 – Trigonometric Integrals
7.1 Integration By Parts.
U-Substitution or The Chain Rule of Integration
7-2 Antidifferentiation by substitution
Integration by Substitution
Miss Battaglia AP Calculus
Hyperbolic & Inverse Hyperbolic Functions
Trig and Hyperbolic Integrals
Warm Up.
6.6 Inverse Trigonometric Functions
Integrals Involving Powers of Sine and Cosine
Logarithmic, Exponential, and Other Transcendental Functions
Inverse Trigonometric Functions: Integration
Intersection of Graphs of Polar Coordinates
Basic Logarithmic and Exponential Integrals
Arc Length and Surface Area
Integration by Parts Lesson 8.2.
7.2 – Trigonometric Integrals
Fundamental Theorem of Calculus Indefinite Integrals
5-6 Derivatives of Inverse Trig Functions
Trigonometric Substitution
More Trigonometric Integrals
Integration.
Integrals Related to Inverse Trig, Inverse Hyperbolic Functions
Integration review.
Average Value of a Function
Clicker Question 1 What is x sin(3x) dx ? A. (1/3)cos(3x) + C
Integration.
Integration by Parts & Trig Functions
Solving Trigonometric Equations
Lesson 7-3 Trig Substitution.
Methods in calculus.
Packet #25 Substitution and Integration by Parts (Again)
Integration by Substitution
The Indefinite Integral
Substitution Lesson 7.2.
Methods in calculus.
Section 3 – Graphing Sine and Cosine Functions
Inverse Trigonometric Functions: Integration
Integration Techniques, L’Hôpital’s Rule, and Improper Integrals
The Natural Log Function: Integration
Hyperbolic Functions Lesson 5.9.
Section 2 Integration by Substitution
Integration and Trig and a bit of Elur Niahc.
Presentation transcript:

The General Power Formula Lesson 9.1

Review From Chapter 6 – General Power Formula Consider application to transcendental functions

Applying Power Formula Consider Let u = sin x u2 = sin2x Then what is du? du = cos x dx

Converting the ln Function Try this … What should we substitute for u? What is the du? The integration u = (ln x) du = 1/x dx

Functions Involving ex Given What should we substitute for u? What is the du? The integration u = 3e3x + 1

Working with Inverse Trig Functions Given What should we substitute for u? What is the du? The integration u = arctan x

Application Find the area under the curve The integral For 0 < x < 1 The integral u = ? du = ?

Assignment Lesson 9.1 Page 357 1 – 27 odd, 31