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Calculus II YouTube Workbook Albert Bronstein Download free books at Albert Bronstein Calculus II YouTube Workbook Download free eBooks at bookboon.com Calculus II YouTube Workbook 1st edition © 2013 Albert Bronstein & bookboon.com ISBN 978-87-403-0470-1 Download free eBooks at bookboon.com Calculus II YouTube Workbook Contents Contents Preface Area Problems Volume by Cross-Section Disk/Washer Method 10 Method of Cylindrical Shells 12 Integration by Parts 14 Trigonometric Integrals 18 Trigonometric Substitution 21 Method of Partial Fraction 24 www.sylvania.com We not reinvent the wheel we reinvent light Fascinating lighting offers an ininite spectrum of possibilities: Innovative technologies and new markets provide both opportunities and challenges An environment in which your expertise is in high demand Enjoy the supportive working atmosphere within our global group and beneit from international career paths Implement sustainable ideas in close cooperation with other specialists and contribute to inluencing our future Come and join us in reinventing light every day Light is OSRAM Download free eBooks at bookboon.com Click on the ad to read more Calculus II YouTube Workbook Contents Arc Length 26 10 Ininite Series Test for Divergence 28 11 Ininite Series Geometric Series 29 12 Ininite Series Telescoping Series 32 13 Ininite Series Integral Test 33 14 Limit Comparison Test 34 360° thinking Discover the truth at www.deloitte.ca/careers Download free eBooks at bookboon.com © Deloitte & Touche LLP and affiliated entities Click on the ad to read more Calculus II YouTube Workbook Preface Preface his workbook contains examples for a standard Calculus II course in an American University Many problems were assigned as homework problems at University of Illinois at Chicago Before viewing solution videos, students should irst try solving these problems on their own Download free eBooks at bookboon.com Calculus II YouTube Workbook Area Problems Area Problems he area of the region bounded by the graphs of y = f (x) and y = g(x) for a ≤ x ≤ b , where f (x) and g (x) are continuous and f (x) ≥ g(x) for all x ∈ [a, b] , is b (f (x) − g(x)) dx a he area of the region bounded by the graphs of x = f (y) and x = g(y) for c ≤ y ≤ d , where f (y) and g (y) are continuous and f (y) ≥ g(y) for all y ∈ [c, d] , is d (f (y) − g(y)) dy c Find the area of the region enclosed by the graphs of f (x) = x and g(x) = x2 ▶ Link to Solution Video ◀ Find the area of the region bounded above by y = √ x + , bounded below by y = x+1 and bounded on the sides by x = and x = ▶ Link to Solution Video ◀ Find the area of the region enclosed by the graphs y = −x2 − 2x + and y = − 2x ▶ Link to Solution Video ◀ Find the area of the region enclosed by the graphs y = 2x2 , y = −4x + and the x-axis ▶ Link to Solution Video ◀ Find the area of the region enclosed by the graphs of y = x − and y = 2x + ▶ Link to Solution Video ◀ Find the area of the region enclosed by the graphs of y = sin x and y = sin 2x for ≤ x ≤ π ▶ Link to Solution Video ◀ Find the area of the region enclosed by the graphs y = x2 − and y = |x| ▶ Link to Solution Video ◀ 10 Evaluate 100 − x2 dx −10 ▶ Link to Solution Video ◀ Download free eBooks at bookboon.com , Calculus II YouTube Workbook Area Problems √ 2/2 Evaluate − ( √ 2/2 − x2 − |x|) dx ▶ Link to Solution Video ◀ 10 Evaluate 24 − 2x − x2 dx −6 ▶ Link to Solution Video ◀ 11 Find the area of the region enclosed by the graphs of x + y = , y = x , and y + 3x = ▶ Link to Solution Video ◀ 12 Find the area of the region enclosed by the graph of y = x3 and the line x = ▶ Link to Solution Video ◀ 13 Find the area of the region enclosed by the graphs of y = ▶ Link to Solution Video ◀ √ x and y = x − x2 14 Find the area of the region enclosed by the graphs of y = x2 − 5x and y = −x2 + x + 20 ▶ Link to Solution Video ◀ 15 Find the area of the region enclosed by the graphs of y = x2 − 5x and y = −x2 + x + 20 for ≤ x ≤ ▶ Link to Solution Video ◀ 16 Evaluate (x + 3) − x2 dx −2 ▶ Link to Solution Video ◀ 17 1Find the area of the region enclosed by the graphs of x = −y + and x = − y − 6y − ▶ Link to Solution Video ◀ 18 Find the area of the region bounded by the graphs of y = x2 , the tangent line to this parabola at the point (1, 1) and the x-axis ▶ Link to Solution Video ◀ Download free eBooks at bookboon.com Calculus II YouTube Workbook Volume by Cross-Section Volume by Cross-Section Let S be a solid that lies between x = a and x = b If the cross-sectional area obtained by intersecting a solid with a plane perpendicular to the x-axis is A(x), where A(x) is a continuous function, then the volume of the solid is b A(x) dx a Let S be a solid that lies between y = c and y = d If the cross-sectional area obtained by intersecting a solid with a plane perpendicular to the y-axis is A(y), where A(y) is a continuous function, then the volume of the solid is d A(y) dy c Find the volume of the solid with a circular base of radius and whose cross-sections perpendicular to the x-axis are equilateral triangles ▶ Link to Solution Video ◀ Find the volume of the solid whose base is a parabolic region {(x, y)|x2 ≤ y ≤ 1} with cross-sections perpendicular to the y-axis are isosceles right triangles with hypotenuse in the base ▶ Link to Solution Video ◀ Find the volume of the solid whose base is bounded by the graphs of 4x + 5y = 20, the x-axis, and the y-axis Cross sections perpendicular to the x-axis are squares ▶ Link to Solution Video ◀ Find the volume of the solid whose base is bounded by the graphs of 4x + 5y = 20, the x-axis, and the y-axis Cross sections perpendicular to the x-axis are semi circles ▶ Link to Solution Video ◀ Find the volume of the solid whose base is bounded by the graph of x2 + y = 2x Cross sections perpendicular to the x-axis are equilateral triangles ▶ Link to Solution Video ◀ Download free eBooks at bookboon.com ...Albert Bronstein Calculus II YouTube Workbook Download free eBooks at bookboon.com Calculus II YouTube Workbook 1st edition © 2013 Albert Bronstein & bookboon.com... affiliated entities Click on the ad to read more Calculus II YouTube Workbook Preface Preface his workbook contains examples for a standard Calculus II course in an American University Many problems... day Light is OSRAM Download free eBooks at bookboon.com Click on the ad to read more Calculus II YouTube Workbook Contents Arc Length 26 10 Ininite Series Test for Divergence 28 11 Ininite Series