# Find the resonance of waves if the function that describe the wave length is f(x)f(x)=sinxcosx

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### 2 Answers

To study the phenomena of resonance, we only need to calculate the indefinite integral of the function that is given.

We have f(x) = sinx * cosx

= sin 2x / 2

Int [ sinx * cosx]

Int [sin 2x / 2 dx]

=> (1/2) Int [ sin 2x dx ]

=> (1/2) -cos 2x / 2

=> (-cos 2x) / 4 +C

Therefore we have - cos 2x / 4 +C

To study the resonance of waves, we'll just have to calculate the indefinite integral of the given function:

f(x) = (sinx)*(cosx)

Int (sinx)*(cosx) dx

We'll use substitution technique:

sin x = t

We'llĀ differentiate:

cos x dx = dt

We'll re-write the function in the variable t:

Int t dt = t^2/2 + C

But t = sin x, so

The system is in resonance if and only if:

**Int (sinx)*(cosx) dx = (sinx)^2/2 + C**