4.4 The Fundamental Theorem of Calculus

Slides:

Advertisements

Similar presentations

Antiderivatives (7.4, 8.2, 10.1) JMerrill, Review Info - Antiderivatives General solutions: Integrand Variable of Integration Constant of Integration.

Advertisements

1 CALCULUS Even more graphing problems

Objective:To use the Fundamental Theorem of Calculus to evaluate definite integrals of polynomial functions. To find indefinite integrals of polynomial.

Areas and Definite Integrals. Objectives Students will be able to Calculate a definite integral. Calculate the area between a curve and the x-axis over.

7.3 Area and The Definite Integral and 7.4 The Fundamental Theorem of Calculus OBJECTIVES  Evaluate a definite integral.  Find the area under a curve.

1 Fundamental Theorem of Calculus Section The Fundamental Theorem of Calculus If a function f is continuous on the closed interval [a, b] and F.

The Fundamental Theorem of Calculus Inverse Operations.

Aim: What is the Fundamental Theorem of Calculus?

4-3 DEFINITE INTEGRALS MS. BATTAGLIA – AP CALCULUS.

Section 5.3 – The Definite Integral

6.3 Definite Integrals and the Fundamental Theorem.

Section 5.3: Evaluating Definite Integrals Practice HW from Stewart Textbook (not to hand in) p. 374 # 1-27 odd, odd.

Warmup 1) 2). 5.4: Fundamental Theorem of Calculus.

THE FUNDAMENTAL THEOREM OF CALCULUS Section 4.4. When you are done with your homework, you should be able to… –Evaluate a definite integral using the.

4.4c 2nd Fundamental Theorem of Calculus. Second Fundamental Theorem: 1. Derivative of an integral.

7.4: The Fundamental Theorem of Calculus Objectives: To use the FTC to evaluate definite integrals To calculate total area under a curve using FTC and.

Section 15.3 Area and Definite Integral

Areas & Definite Integrals TS: Explicitly assessing information and drawing conclusions.

4-4: The Fundamental Theorems Definition: If f is continuous on [ a,b ] and F is an antiderivative of f on [ a,b ], then: The Fundamental Theorem:

4.4 The Fundamental Theorem of Calculus If a function is continuous on the closed interval [a, b], then where F is any function that F’(x) = f(x) x in.

CHAPTER 4 SECTION 4.4 THE FUNDAMENTAL THEOREM OF CALCULUS.

Average Value of a Function and the Second Fundamental Theorem of Calculus Day 2 – Section 5.4 Nancy Powell 2008.

5.4 Fundamental Theorem of Calculus. It is difficult to overestimate the power of the equation: It says that every continuous function f is the derivative.

The Fundamental Theorem of Calculus (4.4) February 4th, 2013.

6/3/2016 Perkins AP Calculus AB Day 10 Section 4.4.

Integration 4 Copyright © Cengage Learning. All rights reserved.

Warm Up – NO CALCULATOR Let f(x) = x2 – 2x.

4-4 THE FUNDAMENTAL THEOREM OF CALCULUS MS. BATTAGLIA – AP CALCULUS.

F UNDAMENTAL T HEOREM OF CALCULUS 4-B. Fundamental Theorem of Calculus If f(x) is continuous at every point [a, b] And F(x) is the antiderivative of f(x)

SECTION 5.4 The Fundamental Theorem of Calculus. Basically, (definite) integration and differentiation are inverse operations.

5.4 Fundamental Theorem of Calculus Quick Review.

Mathematics. Session Definite Integrals –1 Session Objectives  Fundamental Theorem of Integral Calculus  Evaluation of Definite Integrals by Substitution.

SPECIALIST MATHS Calculus Week 6 Definite Integrals & Areas.

Warm-Up: (let h be measured in feet) h(t) = -5t2 + 20t + 15

Miss Battaglia AB/BC Calculus.  Connects differentiation and integration.  Integration & differentiation are inverse operations. If a function is continuous.

FTC Review; The Method of Substitution

The Fundamental Theorem of Calculus

1 Definite Integrals Section The Definite Integral The definite integral as the area of a region: If f is continuous and non-negative on the closed.

4.4 The Fundamental Theorem of Calculus. Essential Question: How are the integral & the derivative related?

5.3 – The Fundamental Theorem of Calculus

4035 Functions Defined by the Definite Integral

5.3 Definite Integrals and Antiderivatives. What you’ll learn about Properties of Definite Integrals Average Value of a Function Mean Value Theorem for.

Warm up Problems More With Integrals It can be helpful to guess and adjust Ex.

Fundamental Theorem of Calculus

Copyright © Cengage Learning. All rights reserved.

The Fundamental Theorem of Calculus is appropriately named because it establishes connection between the two branches of calculus: differential calculus.

4.3 Riemann Sums and Definite Integrals Definition of the Definite Integral If f is defined on the closed interval [a, b] and the limit of a Riemann sum.

CHAPTER Continuity Fundamental Theorem of Calculus In this lecture you will learn the most important relation between derivatives and areas (definite.

5.3 Definite Integrals and Riemann Sums. I. Rules for Definite Integrals.

Definite Integrals. Definite Integral is known as a definite integral. It is evaluated using the following formula Otherwise known as the Fundamental.

5-7: The 1 st Fundamental Theorem & Definite Integrals Objectives: Understand and apply the 1 st Fundamental Theorem ©2003 Roy L. Gover

4.3 Riemann Sums and Definite Integrals

Essential Question: How is a definite integral related to area ?

(MTH 250) Lecture 19 Calculus. Previous Lecture’s Summary Definite integrals Fundamental theorem of calculus Mean value theorem for integrals Fundamental.

The Fundamental Theorem of Calculus Area and The Definite Integral OBJECTIVES  Evaluate a definite integral.  Find the area under a curve over a given.

THE FUNDAMENTAL THEOREM OF CALCULUS Section 4.4. THE FUNDAMENTAL THEOREM OF CALCULUS Informally, the theorem states that differentiation and definite.

Calculus 4-R Unit 4 Integration Review Problems. Evaluate 6 1.

Mean Value Theorem 5.4.

4.4 The Fundamental Theorem of Calculus

4.4 The Fundamental Theorem of Calculus

MTH1170 The Fundamental Theorem of Calculus

Area and the Fundamental Theorem of Calculus

4.4 The Fundamental Theorem of Calculus

Integration Review Problems

Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. {image}

Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. {image}

Integrations and Its Applications

THE FUNDAMENTAL THEOREM OF CALCULUS

Integrations and Its Applications

4.4 The Fundamental Theorem of Calculus

Presentation transcript:

4.4 The Fundamental Theorem of Calculus

Evaluating a Definite Integral Evaluate each definite integral.

A definite integral involving absolute value

Using the fundamental theorem to find area Find the area of the region bounded by the graph , the x-axis, and the vertical lines x=0 and x=2.

Using Mean Value Theorem Find the values of c guaranteed by the mean value theorem for integrals over the given interval.

Finding the Average Value of a Function Find the average value of on the interval [1,4].

The Definite Integral as a Function Evaluate the function at

Using the Second Fundamental Theorem of Calculus

Using the Second Fundamental Theorem of Calculus Find the derivative of