TOPICS
This page:
integration
About Levels
of Difficulty
Trigonometry
law of sines
law of cosines
Calculus
derivatives
integration
series
Trig/Calculus
proof
area
perimeter
volume
Browse all
Trig/Calc
Problems
Trig/Calc
Home
About the
PoW Library

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 heartshaped 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 crosssection of an egg given some dimensions of the crosssection.
... 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 6ft by 100ft 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 nonoverlapping 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 parabolashaped 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
