CK-12-Calculus

4.7. Integration by Substitution http://www.ck12.org ∫ √ udu=^23 u^32 +C=^23 ( √ 1 +x^3 )^32 +C. While this method of substituti ...

http://www.ck12.org Chapter 4. Integration Integrating Products of Functions We are not able to state a rule for integrating pro ...

4.7. Integration by Substitution http://www.ck12.org Review Questions Compute the integrals in problems #1–10. 1.∫xlnxdx 2.∫ 13 ...

http://www.ck12.org Chapter 4. Integration 4.8 Numerical Integration Learning Objectives Use the Trapezoidal Rule to solve prob ...

4.8. Numerical Integration http://www.ck12.org The area of a trapezoid isA=h(b^12 +b^2 ), whereb 1 andb 2 are the lengths of the ...

http://www.ck12.org Chapter 4. Integration issue concerns the questions about the accuracy of the approximation. In particular, ...

4.8. Numerical Integration http://www.ck12.org Using parabolas in this way produces the following estimate of the area from Simp ...

http://www.ck12.org Chapter 4. Integration Solution: We need to findnsuch that|Errorsim pson|≤ 0. 001 .We start by noting that∣∣ ...

4.8. Numerical Integration http://www.ck12.org We estimated errors for the Trapezoidal Rule. We used Simpson’s Rule to solve pr ...

http://www.ck12.org Chapter 5. Applications of Definite Integrals CHAPTER 5 Applications of Definite Integrals Chapter Outline 5 ...

5.1. Area Between Two Curves http://www.ck12.org 5.1 Area Between Two Curves Learning Objectives A student will be able to: Com ...

http://www.ck12.org Chapter 5. Applications of Definite Integrals Figure 1b Figure 1c Therefore, as the graphs show, it makes se ...

5.1. Area Between Two Curves http://www.ck12.org A= ∫b a[f(x)−g(x)]dx. Example 1: Find the area of the region enclosed betweeny= ...

http://www.ck12.org Chapter 5. Applications of Definite Integrals A= ∫b a[f(x)−g(x)]dx = ∫ 3 − 2 [(x+^6 )−(x (^2) )]dx. Integrat ...

5.1. Area Between Two Curves http://www.ck12.org Find the area of the region enclosed byx=y^2 andy=x− 6. Solution: Figure 4 As y ...

http://www.ck12.org Chapter 5. Applications of Definite Integrals MEDIA Click image to the left for use the URL below. URL: http ...

5.2. Volumes http://www.ck12.org 5.2 Volumes Learning Objectives Learn the basic concepts of volume and how to compute it with ...

http://www.ck12.org Chapter 5. Applications of Definite Integrals The volume of solid does not necessarily have to be circular. ...

5.2. Volumes http://www.ck12.org If we use the same argument to derive a formula to calculate the area under the curve, let us i ...

http://www.ck12.org Chapter 5. Applications of Definite Integrals Figure 7a Figure 7b Solution: Let they−axis pass through the a ...