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Question
If `int_0^(2π) cos^2 x dx = k int_0^(π/2) cos^2 x dx`, then the value of k is ______.
Options
4
2
1
0
Solution
If `int_0^(2π) cos^2 x dx = k int_0^(π/2) cos^2 x dx`, then the value of k is 4.
Explanation:
`int_0^(2π) cos^2 x dx = k int_0^(π/2) cos^2 x dx`
Taking LHS = `int_0^(2π) cos^2 x dx`
= `2int_0^π cos^2 x dx` ...[∵ cos2 x is an even function]
= `2 xx 2int_0^(π/2) cos^2 x dx` ...[∵ cos2 x is an even function]
= `4int_0^(π/2) cos^2 x dx`
On comparing both sides, we get
k = 4.
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