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Determine the following integrals: 1.1 G 3x³ +8 X dx 1.2 G 1.3 4x+6 dx x + 3x-10 sec² (sin 5x)cos 5x dx dx

Determine the following integrals: 1.1 G 3x³ +8 X dx 1.2 G 1.3 4x+6 dx x + 3x-10 sec² (sin 5x)cos 5x dx dx

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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QUESTION 1 Determine the following integrals: 3x³ +8 1.1 dx X 4x+6 1.2 dx x + 3x-10 1.3 sec²(sin 5x)cos 5x dx dx 1.4 √en(3)+2x 4 dx 1.5 en( e³x) 2 Show steps. Your reasoning is more important than the numerical answer. QUESTION 2 Note the word curve is used to indicate a graph and can be for example a straight line, parabola ellipse, hyperbola etc. 2.1 Find the area enclosed by the curves y=x² - 4x+3 and y=0 between the y-axis and x = 3. Reflection: 2.2 Why is a sketch essential to determine areas between curves? 2.3 What do you understand under the term "absolute value"? QUESTION 3 Suppose that liquid flows into a tank at a variable rate of q(t) litre per second. It can be shown that the area under the graph of q against t represents the volume of liquid in the tank. Consider a chemical storage tank with liquid entering at a rate of q(t) = 6 - + t ť 10 100 If at time t = 0 the tank is empty, calculate the volume of liquid in the tank at time t = 20 seconds. Į
Transcribed Image Text:QUESTION 1 Determine the following integrals: 3x³ +8 1.1 dx X 4x+6 1.2 dx x + 3x-10 1.3 sec²(sin 5x)cos 5x dx dx 1.4 √en(3)+2x 4 dx 1.5 en( e³x) 2 Show steps. Your reasoning is more important than the numerical answer. QUESTION 2 Note the word curve is used to indicate a graph and can be for example a straight line, parabola ellipse, hyperbola etc. 2.1 Find the area enclosed by the curves y=x² - 4x+3 and y=0 between the y-axis and x = 3. Reflection: 2.2 Why is a sketch essential to determine areas between curves? 2.3 What do you understand under the term "absolute value"? QUESTION 3 Suppose that liquid flows into a tank at a variable rate of q(t) litre per second. It can be shown that the area under the graph of q against t represents the volume of liquid in the tank. Consider a chemical storage tank with liquid entering at a rate of q(t) = 6 - + t ť 10 100 If at time t = 0 the tank is empty, calculate the volume of liquid in the tank at time t = 20 seconds. Į
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