definite integral3 Calculus 1 Summary Notes [Chapter 1. FOUNDATION FOR CALCULUS: FUNCTIONS & LIMITS] 1.1 Functions and Change 1.2 Exponential Functions 1.3 New Functions from Old 1.4 Logarithmic Functions 1.5 Trigonometric Functions 1.6 Powers, Polynomials, and Rational Functions 1.7 Introduction to Limits and Continuity 1.8 Extending the Idea of a Limit [Chapter 2. KEY CONCEPT: THE DERIVATIVE] 2.1 How Do We Measure Speed? 2.2 The Derivat.. 2022. 12. 13. [Notes & HW Answers] 5.4 Theorems about Definite Integral [Prepwork 5.4] Q1. For some function f, suppose that for some a∫^b_a f(x) dx=7 and ∫^c_a f(x) dx=9. Find each of the following. A: ∫^a_b f(x) dx= −7 ;∫^c_b f(x) dx= 2 Q2. Use the technique of example 2 in the text to evaluate the integral ∫^2_(−2) (|2x|+3) dx exactly. A: ∫^2_−2 (|2x|+3) dx = 20 Q3. Using a calculator to evaluate the appropriate integral, find the average value of P = f(t) = 2.03.. 2022. 12. 6. [Notes & HW Answers] 5.2 The Definite Integral [Prepwork 5.2] Q1. Following example 1 in the text, suppose we considered n=4 to approximate the integral. What are each of the following? A: Δt= 0.25; f(t2)= 1/1.5 Q2. Find the exact value of the following integral. A: ∫^2_(-2) (4-x^2)^(1/2) dx = 2π Estimate the total area between f(x)=cos(x4) and the x-axis for (0≤x≤π)^(1/4)(Note: you will want to sketch the curve y=f(x). Shade the regions be.. 2022. 12. 6. 이전 1 다음
