Question

integration

sin 7x cos 3x​

Answer 1

Answer:

Rewriting the expression as

Sin(7x) + Sin (Pi/2 - 3x)

and using the identity

Sin (A) + Sin(B) = 2 Sin[(A+B)/2] Cos[(A- B)/2]

we have

2 Sin(2x + Pi/4).Cos (5x - Pi/4) = 0.

Conclusion:

Either 2x + Pi/4 = m Pi

or 5x - Pi/4 = (n + 1/2) Pi,

( m, n integers).

For instance,

m = 0 yields x = - Pi/8,

m = 2 yields x = (7/8) Pi etc.

Step-by-step explanation:

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