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[email protected]
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#1
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#1
Int. 2/ cos^2(0.5x)

The answer is 4tan(0.5x)

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Jonny W
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#2
Report 14 years ago
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y = 0.5x
dy/dx = 0.5

(int) 2/cos^2(0.5x) dx
= (int) 4/cos^2(y) dy
= (int) 4 sec^2(y) dy
= 4 tan(y) + c
= 4 tan(0.5x) + c
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Nima
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#3
Report 14 years ago
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(Original post by [email protected])
Int. 2 / cos^2(0.5x) dx
Firstly take note of this important fact:
d/dx (tanx) = sec^2x ---> Int sec^2x = tanx

Hence:
Int. 2/cos^2(0.5x) dx
= Int 2sec^2(0.5x) dx {NB: 1/cos^2x = sec^2x}
= (2/0.5)tan(0.5x) + k
= 4tan(0.5x) + k
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