1 Functions And Models 2 Limits And Derivatives 3 Differentiation Rules 4 Applications Of Differentiation 5 Integrals 6 Applications Of Integration 7 Techniques Of Integration 8 Further Applications Of Integration 9 Differential Equations 10 Parametric Equations And Polar Coordinates 11 Sequences, Series, And Power Series 12 Vectors And The Geometry Of Space 13 Vector Functions 14 Partial Derivatives 15 Multiple Integrals 16 Vector Calculus A Numbers, Inequalities, And Absolute Values B Coordinate Geometry And Lines C Graphs Of Second-degree Equations D Trigonometry E Sigma Notation F Proofs Of Theorems G The Logarithm Defined As An Integral expand_more
8.1 Arc Length 8.2 Area Of A Surface Of Revolution 8.3 Applications To Physics And Engineering 8.4 Applications To Economics And Biology 8.5 Probability Chapter Questions expand_more
Problem 1E: The given curve is rotated about the x -axis. Set up, but do not evaluate, an integral for the area... Problem 2E: The given curve is rotated about the x -axis. Set up, but do not evaluate, an integral for the area... Problem 3E: The given curve is rotated about the x -axis. Set up, but do not evaluate, an integral for the area... Problem 4E: The given curve is rotated about the x -axis. Set up, but do not evaluate, an integral for the area... Problem 5E: The given curve is rotated about the y -axis. Set up, but do not evaluate, an integral for the area... Problem 6E: The given curve is rotated about the y -axis. Set up, but do not evaluate, an integral for the area... Problem 7E: The given curve is rotated about the y -axis. Set up, but do not evaluate, an integral for the area... Problem 8E Problem 9E: Find the exact area of the surface obtained by rotating the curve about the x-axis. 7. y = x3, 0 x ... Problem 10E: Find the exact area of the surface obtained by rotating the curve about the x-axis. 8. y=5x, 3 x 5 Problem 11E: Find the exact area of the surface obtained by rotating the curve about the x-axis. 9. y2 = x + 1, 0... Problem 12E: Find the exact area of the surface obtained by rotating the curve about the x-axis. 10. y=1+ex, 0 x... Problem 13E: Find the exact area of the surface obtained by rotating the curve about the x-axis. 11. y=cos(12x),... Problem 14E: Find the exact area of the surface obtained by rotating the curve about the x-axis. 12. y=x36+12x,... Problem 15E: Find the exact area of the surface obtained by rotating the curve about the x-axis. 13.... Problem 16E: Find the exact area of the surface obtained by rotating the curve about the x-axis. 14. x = 1 + 2y2,... Problem 17E: The given curve is rotated about the y-axis. Find the area of the resulting surface. 15. y=13x3/2, 0... Problem 18E: The given curve is rotated about the y-axis. Find the area of the resulting surface. 16.... Problem 19E: The given curve is rotated about the y-axis. Find the area of the resulting surface. 17. x=a2y2, 0 ... Problem 20E: The given curve is rotated about the y-axis. Find the area of the resulting surface. 18.... Problem 21E Problem 22E Problem 23E Problem 24E Problem 25E Problem 26E Problem 27E Problem 28E: Find the exact area of the surface obtained by rotating the given curve about the x -axis. 28.... Problem 29E Problem 30E Problem 31E: Use Simpsons Rule with n = 10 to approximate the area of the surface obtained by rotating the curve... Problem 32E: Use Simpsons Rule with n = 10 to approximate the area of the surface obtained by rotating the curve... Problem 33E Problem 34E: If the infinite curve y = ex, x 0, is rotated about the x-axis, find the area of the resulting... Problem 35E Problem 36E Problem 37E: (a) The ellipse x2a2+y2b2=1ab is rotated about the x-axis to form a surface called an ellipsoid, or... Problem 38E Problem 39E Problem 40E Problem 41E: Find the area of the surface obtained by rotating the circle x2 + y2= r2 about the line y = r. Problem 42E Problem 43E Problem 44E Problem 45E: Show that if we rotate the curve y = ex/2 + e x/2 about the x-axis, the area of the resulting... Problem 46E: Formula 4 is valid only when f(x) 0. Show that when f(x) is not necessarily positive, the formula... Problem 1DP Problem 2DP Problem 3DP Problem 4DP Problem 5DP Problem 6DP format_list_bulleted