2. (a) Let r> 0 and ro € R. Compute Hint: Consider ₁ √√1 – x²dæ first. = √r² — (x − r)² - (b) Let r > 0 and denote by A, the area bounded by the curves y and x = √r² − (y — r)² in the first quadrant (see Figure below). Compute y-axis Hint: The points at which the two curves intersect are of the form (a, a) for a > 0. Find a! 5 4 3- 2- 1 rxo+r 12 [2007 √r² - (x − xo)²dx. r xo-r 0 1 y = sqrt(r^2 - (x-r)^2) x = sqrt(r^2-(y-r)^2) Area Ar 1 7.2 Area(Ar). Plot of A, for r = 5 T 2 x-axis 3 5
2. (a) Let r> 0 and ro € R. Compute Hint: Consider ₁ √√1 – x²dæ first. = √r² — (x − r)² - (b) Let r > 0 and denote by A, the area bounded by the curves y and x = √r² − (y — r)² in the first quadrant (see Figure below). Compute y-axis Hint: The points at which the two curves intersect are of the form (a, a) for a > 0. Find a! 5 4 3- 2- 1 rxo+r 12 [2007 √r² - (x − xo)²dx. r xo-r 0 1 y = sqrt(r^2 - (x-r)^2) x = sqrt(r^2-(y-r)^2) Area Ar 1 7.2 Area(Ar). Plot of A, for r = 5 T 2 x-axis 3 5
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Transcribed Image Text:2. (a) Let r> 0 and ro € R. Compute
Hint: Consider ₁ √√1 – x²dæ first.
=
√r² — (x − r)²
-
(b) Let r > 0 and denote by A, the area bounded by the curves y
and x =
√r² − (y — r)² in the first quadrant (see Figure below). Compute
y-axis
Hint: The points at which the two curves intersect are of the form (a, a) for a > 0.
Find a!
5
4
3-
2-
1
rxo+r
12 [2007 √r² - (x − xo)²dx.
r
xo-r
0
1
y = sqrt(r^2 - (x-r)^2)
x = sqrt(r^2-(y-r)^2)
Area Ar
1
7.2 Area(Ar).
Plot of A, for r = 5
T
2
x-axis
3
5
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