Question

Evaluate The Integral: Sin 3x Cos 7x Dx?

Answer 1

Answer:

Although we have a product in the integrand, it is not necessary to use integration by parts, you can use the trigonometric identity

cos(α)sin(β)=12(sin(α−β+sin(α+β)cos⁡(α)sin⁡(β)=12(sin⁡(α−β)+sin⁡(α+β) and use a substitution after that you will find ur answer...

Answer 2

Answer:

(cos4x)/8 + C -(cos10x)/10

Step-by-step explanation:

We know,

sin(a+b) = sina.cosb + sinb.cosa

and, sin(a-b) = sinb.cosa - sinb.cosa

∴ sin(a+b) - sin(a-b) =  2sinb.cosa

 = sinb.cosa = 1/2(sin(a+b) + sin(a-b))

So, sin3x.cos7x = 1/2(sin(7x+3x) - sin(7x-3x))

= 1/2(sin(10x) - sin(4x))

∴ ∫ sin3x.cos7x dx = ∫ 1/2(sin10x - sin4x)

= -1/2((cos10x)/10 - (cos4x)/4) + C = -(cos10x)/10 + (cos4x)/8 + C

= (cos4x)/8 - (cos10x)/10 + C

Hope, you got it:-))

Please, mark it as brainiest!!