Math Forum - Problems Library - Trig/Calculus, Integration

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 TOPICS This page:   integration  Trigonometry   law of sines   law of cosines Calculus   derivatives   integration   series Trig/Calculus   proof   area   perimeter   volume Calculus: Integration Integration is a primary topic in most second semester calculus courses. There are four applications of integration that can be found below -- finding areas (as in Ellipse Areas), finding volumes (Cup Capacity), differential equations (Vehicle Value), and arc length (Painting the Sin Curve). For background information elsewhere on our site, explore the High School Calculus area of the Ask Dr. Math archives. For example, the archives provide information on integrals and the fundamental theorem of calculus. To find relevant sites on the Web, browse and search Calculus (Single Variable): Integration in our Internet Mathematics Library. Access to these problems requires a Membership. Be My Valentine - Leigh Nataro Trig/Calc, difficulty level 4. Find the areas of two heart-shaped valentines. ... more>> Cooling Colas - Leigh Nataro Trig/Calc, difficulty level 3. Use Newton's Law of cooling to determine when the colas will freeze. ... more>> Cup Capacity - Leigh Nataro Trig/Calc, difficulty level 3. Find the volume of a cup based on its dimensions. ... more>> Cutting the Cookie - Leigh Nataro Trig/Calc, difficulty level 2. Where should you cut a circular cookie so its area is in a ratio of 1:2 ? ... more>> Doughnut Dilemma - Leigh Nataro Trig/Calc, difficulty level 2. Which doughnut shop makes a doughnut with a greater volume? ... more>> An Eggstra Special Problem - Leigh Nataro Trig/Calc, difficulty level 2. Find the area of a cross-section of an egg given some dimensions of the cross-section. ... more>> Ellipse Areas - Leigh Nataro Trig/Calc, difficulty level 3. Use calculus to show that the area of an ellipse is pi*a*b. ... more>> Find the Function - Leigh Nataro Trig/Calc, difficulty level 3. Find a cubic polynomial that has a given maximum, minimum, and point of inflection. ... more>> Five Golden Rings - Leigh Nataro Trig/Calc, difficulty level 5. Based on the given information, find the volume of five golden rings. ... more>> Football Volume - Leigh Nataro Trig/Calc, difficulty level 3. Given the dimensions of a football, find its volume. ... more>> Googol the Giant's Gargantuan Goblet - Leigh Nataro Trig/Calc, difficulty level 2. Find the volume of Googol the Giant's elliptical paraboloid goblet. ... more>> My Hot Chocolate is Too Hot! - Leigh Nataro Trig/Calc, difficulty level 3. Use Newton's Law of Cooling to determine how long it will take for your hot chocolate to cool. ... more>> Needles and Lines - Leigh Nataro Trig/Calc, difficulty level 5. Use trigonometry and calculus to find the probability of a needle touching a line. ... more>> One Area - Many Solutions - Leigh Nataro Trig/Calc, difficulty level 2. Find the area of a triangle given the coordinates of its vertices. ... more>> The Oval Braided Rug - Leigh Nataro Trig/Calc, difficulty level 2. Find the area of a shaded portion of an ellipse. ... more>> Painting the Sine Curve - Leigh Nataro Trig/Calc, difficulty level 4. Find the length of the sine curve that would fill a 6-ft by 100-ft rectangle. ... more>> A Parabola Proof - Leigh Nataro Trig/Calc, difficulty level 3. Prove that the area of a parabola is 2/3 the product of its width and height. ... more>> A Picture Is Worth A Thousand Words - Leigh Nataro Trig/Calc, difficulty level 4. Find the ratio of the area of the overlapping region to the area of non-overlapping regions of two circles. ... more>> The Square and the Line - Leigh Nataro Trig/Calc, difficulty level 1. Find the equation of the line that will split a unit square into two pieces that have equal areas. ... more>> The Suspension Bridge - Leigh Nataro Trig/Calc, difficulty level 4. Determine the length of a parabola-shaped cable on a suspension bridge. ... more>> That's A Lot of Rock! - Leigh Nataro Trig/Calc, difficulty level 3. Find the volume of a tunnel through a mountain. ... more>> Time to Make the Doughnuts - David Turner Trig/Calc, difficulty level 4. Find the radius of a doughnut with center at (0, 10) and a volume of 3158 cubic centimeters. ... more>> Vehicle Value - Leigh Nataro Trig/Calc, difficulty level 2. Find the future value of a car based on its current price and initial selling price. ... more>> Page:  1