1)] Archimedes used the sum of a geometric scries to compute the arca enclosed by a parabola and a straight line. His method was to dissect the arca into an infinite number of triangles. Archimedes determined that cach green triangle has 1/8 the arca of the blue triangle, cach yellow triangle has 1/8 the arca of a green triangle, and so forth. Assuming that the blue triangle has arca 1, the total arca of the shaded region is the infinite sum:
1)] Archimedes used the sum of a geometric scries to compute the arca enclosed by a parabola and a straight line. His method was to dissect the arca into an infinite number of triangles. Archimedes determined that cach green triangle has 1/8 the arca of the blue triangle, cach yellow triangle has 1/8 the arca of a green triangle, and so forth. Assuming that the blue triangle has arca 1, the total arca of the shaded region is the infinite sum:
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![1)] Archimedes used the sum of a geometric series to compute the arca enclosed by a parabola and
a straight linc. His method was to dissect the arca into an infinite number of triangles. Archimedes
determined that each green triangle has 1/8 the arca of the blue triangle, cach yellow triangle has 1/8
the arca of a green triangle, and so forth. Assuming that the blue triangle has arca 1, the total area of
the shaded region is the infinite sum:](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa187ce5a-3d82-43aa-a3a1-ae06a14e5bec%2Ffac28751-b519-4a39-b219-9e761e6f097f%2Fsh3zz88_processed.png&w=3840&q=75)
Transcribed Image Text:1)] Archimedes used the sum of a geometric series to compute the arca enclosed by a parabola and
a straight linc. His method was to dissect the arca into an infinite number of triangles. Archimedes
determined that each green triangle has 1/8 the arca of the blue triangle, cach yellow triangle has 1/8
the arca of a green triangle, and so forth. Assuming that the blue triangle has arca 1, the total area of
the shaded region is the infinite sum:
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