Kahwai's answer to Candice's Junior College 1 H2 Maths Singapore question.
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Part 1
Let y = 2 sintheta
dy = 2 costheta dtheta
Original becomes integral of
2 (1-cos^2theta)^0.5
= 2 |sintheta|
From the range check whether sintheta is positive or negative
And integrate
Part 2
T = tantheta => arTan(t) is theta
dTheta = 1/(1+ t^2) dt
Sintheta is t/(1 + t^2)^0.5
Integrate
t . (1+t^2)^(-1.5)
(1+t^2)^(-1.5+1)/(2 . (-0.5)) + C
Then find answers
Let y = 2 sintheta
dy = 2 costheta dtheta
Original becomes integral of
2 (1-cos^2theta)^0.5
= 2 |sintheta|
From the range check whether sintheta is positive or negative
And integrate
Part 2
T = tantheta => arTan(t) is theta
dTheta = 1/(1+ t^2) dt
Sintheta is t/(1 + t^2)^0.5
Integrate
t . (1+t^2)^(-1.5)
(1+t^2)^(-1.5+1)/(2 . (-0.5)) + C
Then find answers
Date Posted:
4 years ago
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