# Definite Integrals Questions and Answers

Calculus

Definite IntegralsLet f x x 3x 189x 6 Use the definition of a derivative or the derivative rules to find f x f x Use the definition of a derivative or the derivative rules to find f x f x On what interval is f increasing do not include the endpoints in the interval Interval on which f is increasing On what interval is f decreasing do not include the endpoints in the interval Interval on which f is decreasing On what interval is f concave down do not include the endpoints in the interval Interval of downward concavity On what interval is f concave up do not include the endpoints in the interval Interval of upward concavity

Calculus

Definite IntegralsUse the sum of the first 10 terms to approximate the sum 5 of the series Round your answers to six decimal places Sn n 3 3 x Estimate the error S 10 S n 1 3

Calculus

Definite Integrals5 16 Solving Basic Trigonometric Equations S equation 5 sin 0 V3 2 6 sin 0

Calculus

Definite IntegralsOf the people who fished at Clearwater Park today 48 had a fishing license and 12 did not Of the people who fished at Mountain View Park today 40 had a license and 10 did not No one fished at both parks Suppose that one fisher from each park is chosen at random What is the probability that the fisher chosen from Clearwater had a license and the fisher chosen from Mountain View did not have a license Do not round your answer If necessary consult a list of formulas

Calculus

Definite IntegralsWhat is the domain of g x y OB x y x 1 Select the correct choice below and fill in any answer boxes within your choice OA x y y Use a comma to separate answers as needed OC x y x xy Use a comma to separate answers as needed OD R and y Use a comma to separate answers as needed

Calculus

Definite Integrals2 a Find the area of the region inside r 3a cos 0 but outside r a a cos 0 where a is some positive constant b Graph the set of points whose polar coordinates satisfy 0 7 2 r 2 6 c Convert the polar equation r sin 0 6 into Cartesian coordinates and sketch it

Calculus

Definite Integrals6 Pts total Given the integral Q f 4y 2x dydx a 4 Points Rewrite the given integral REVERSING the order of integration Be sure to draw a NEAT well labelled diagram of R showing a windshield wiper corresponding to the NEW order of integration b 2 Points Perform the integration using the new order IF you are unable to perform part a complete the integration in the given order Max credit 1 point

Calculus

Definite IntegralsIn a trend that scientists attribute at least in part to global warming a certain floating cap of sea ice has been shrinking since 1980 The ice cap always shrinks in the summer and grows in winter Average minimum size of the ice cap in square miles can be approximated by A r In 2013 the radius of the ice cap was approximately 793 and was shrinking at a rate of approximately 4 1 mi yr How fast was the area changing at that time The area was changing at a rate of Round to the nearest integer as needed in 2013 mi yr mi yr yr mi mi yr mi yr

Calculus

Definite Integralsse the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by the curves y x and y about the line y 1 olume

Calculus

Definite Integrals75 We know from Example 1 that the region x y x 1 0 y 1 x has infinite area Show that by rotating about the x axis obtain a solid called Gabriel s horn with finite volume