iCoachMath.com: Examples on Limits and Motion: The Area Problem - An Introduction to Calculus: Limits, Derivatives, and Integrals - (AL)
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Solved Examples

Curriculum: Alabama Course of Study   Click to change Curriculum

Topic: An Introduction to Calculus: Limits, Derivatives, and Integrals  Click to change Topic

Lesson: 10: Limits and Motion: The Area Problem  Click to change Lesson

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eee The rate of flow of water from a pump is 40 gal/min. Find the number of gallons it pumps in 5 hours.
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eee An airplane travels for 3 hours, at an average velocity of 360 km per hour. Find the distance travelled by the plane. eee View Solution
eee The population density of a small country is 400 people per square mile.Find the population of the country, if its area is 60,000 square miles. eee View Solution
eee The rate of flow of water from a pump is 50 gal/min. Find the number of gallons it pumps in 5 hours.
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eee Approximate the area of the region below the graph over the interval [0, 1] by using PRAM.[Use 4 rectangles.]
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eee Approximate the area of the region under the curve over the interval [0, 6] by using LRAM.[Use 11 rectangles.]
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eee The population density of a small country is 400 people per square mile.Find the population of the country, if its area is 40,000 square miles. eee View Solution
eee The rate of flow of water from a reservoir is 200 cubic feet per second. Find the volume of the water that flows out in 3 hours.
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eee Approximate the area of the region below the graph over the interval [0, 2] by using LRAM.[Use 7 rectangles.] eee View Solution
eee Approximate the area of the region below the graph over the interval [0, 2] by using PRAM.[Use 8 rectangles.]
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eee Approximate the area of the region below the graph over the interval [1, 7] by using RRAM.[Use 12 rectangles.]
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eee Approximate the area of the region below the graph over the interval [-2, 2] by using PRAM.[Use 8 rectangles.]
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eee Find the area under the curve from the given graph over the interval [1, 4] by using PRAM.[Use 6 rectangles.]
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eee An airplane travels for 5 hours, at an average velocity of 640 km per hour. Find the distance travelled by the plane. eee View Solution
eee Approximate the area of the region below the graph of f (x) = - x2 + 4x over the interval [0, 2] by using PRAM.[Use 8 rectangles.]
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eee Approximate the area of the region below the graph of y = x2 over the interval [0, 2] by using PRAM.[Use 7 rectangles.]
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eee Approximate the area of the region below the graph of y = x4 - 3x3 + 2x2 + 5x over the interval [0, 2] by using PRAM.[Use 8 rectangles.]
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eee Find the definite integral ∫162xdx by using LRAM.[Use 10 rectangles.]
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eee Find the definite integral ∫13(x2 + 5)dx by using LRAM.[Use 4 rectangles.]
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DD  Find ∫27(x3 + 2x)dx by using LRAM.[Use 10 rectangles.]
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DD  Find ∫14(2x + 5)dx by using PRAM.[Use six rectangles.]
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DD  Find ∫14(4 - x)dx by using PRAM.[Use 6 rectangles.]
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DD  Find ∫282x dx by PRAM.[Use 6 rectangles.]
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DD  Find ∫151x dx by computing the area using PRAM.[Use 8 rectangles.]
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DD  Approximate the area under the given curve over the interval [-2, 2] by using 8 rectangles using LRAM.
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DD  Find ∫143xdx by computing area using PRAM. [Use 6 rectangles.]
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DD  The length of a metal rod is incresing at the rate of 0.1 cm/hour on heating.Find the increase in its length when it is heated for 20 min.
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DD  The rate of flow of water from a reservoir is 500 cubic feet per second. Find the volume of the water that flows out in 5 hours.
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DD  Which of the following is true, while estimating the area under a curve?
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