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SUROJ
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Anybody know how to find the integral of following figure?
 2 years ago
 2 years ago
SUROJ Group Title
Anybody know how to find the integral of following figure?
 2 years ago
 2 years ago

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SUROJ Group TitleBest ResponseYou've already chosen the best response.0
dw:1352073105071:dw
 2 years ago

SUROJ Group TitleBest ResponseYou've already chosen the best response.0
I mean area of the triangle using polar coordinates
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.0
using a double integral?
 2 years ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.1
rcostheta + rsintheta =1 r=1/(costheta +sintheta) \[\int\limits_{0}^{\frac{ \pi }{ 2 }} \frac{ r^2 }{2 } d \theta = \frac{ 1 }{ 2 }\int\limits_{0}^{\frac{ \pi }{ 2 }} \frac{ 1 }{(\cos \theta +\sin \theta )^2} d \theta \]
 2 years ago

SUROJ Group TitleBest ResponseYou've already chosen the best response.0
@TuringTest yes @Algebraic! how did u got that? can you explain some more?
 2 years ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.1
x=rcostheta y=rsintheta
 2 years ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.1
area = integral (r^2)/2 d theta
 2 years ago

sirm3d Group TitleBest ResponseYou've already chosen the best response.0
the differential of of the area of a sector is given by \[dA=\frac{ 1 }{ 2 }r^2 d \theta \] so the area of the region is a definite integral \[A=\int\limits_{a}^{b}\frac{ 1 }{ 2 }r^2 d \theta \].
 2 years ago

SUROJ Group TitleBest ResponseYou've already chosen the best response.0
dw:1352074998837:dw
 2 years ago

SUROJ Group TitleBest ResponseYou've already chosen the best response.0
but we need to find area of triangle
 2 years ago

SUROJ Group TitleBest ResponseYou've already chosen the best response.0
@Algebraic! isn't that integral from 0 to pi/4
 2 years ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.1
are you in calc. 2?
 2 years ago

SUROJ Group TitleBest ResponseYou've already chosen the best response.0
Oh yea it's pi/2 thnks @Algebraic! ......but why dA is r^2/s d(theta)
 2 years ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.1
because the area of a circular sector is r^2 /2 times theta
 2 years ago

SUROJ Group TitleBest ResponseYou've already chosen the best response.0
Finally I got it thnks guys
 2 years ago

sirm3d Group TitleBest ResponseYou've already chosen the best response.0
dw:1352076292545:dw the small triangle is approximated by a sector of a circle.
 2 years ago
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