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Question
`int_((-pi)/4)^(pi/4) "dx"/(1 + cos2x)` is equal to ______.
Options
1
2
3
4
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Solution
`int_((-pi)/4)^(pi/4) "dx"/(1 + cos2x)` is equal to 1.
Explanation:
Let I = `int_((-pi)/4)^(pi/4) "dx"/(1 + cos2x)`
= `int_((-pi)/4)^(pi/4) "dx"/(2cos^2x)`
= `1/2 int_((-pi)/4)^(pi/4) sec^2x "d"x`
= `1/2 [tan x]_((-pi)/4)^(pi/4)`
= `1/2 [tan pi/4 - tan (- pi/4)]`
= `1/2[1 + 1]`
= `1/2 xx 2`
= 1
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