Solution Found!
Archimedes’ area formula for parabolic arches Archimedes
Chapter 5, Problem 71E(choose chapter or problem)
Problem 71E
Archimedes’ area formula for parabolic arches Archimedes (287–212 B.C.), inventor, military engineer, physicist, and the greatest mathematician of classical times in the Western world, discovered that the area under a parabolic arch is two-thirds the base times the height. Sketch the parabolic arch y = h – (4h/b2)x2, -b/2 ≤ x ≤ b/2, assuming that h and b are positive. Then use calculus to find the area of the region enclosed between the arch and the x-axis.
Questions & Answers
QUESTION:
Problem 71E
Archimedes’ area formula for parabolic arches Archimedes (287–212 B.C.), inventor, military engineer, physicist, and the greatest mathematician of classical times in the Western world, discovered that the area under a parabolic arch is two-thirds the base times the height. Sketch the parabolic arch y = h – (4h/b2)x2, -b/2 ≤ x ≤ b/2, assuming that h and b are positive. Then use calculus to find the area of the region enclosed between the arch and the x-axis.
ANSWER:
SOLUTION
Step 1 of 4
Here, we are asked to sketch the parabolic arc , assuming that h and b are positive.
Then, we have to find the area of the region enclosed between the arch and the x-axis.