Evaluate-I-ab-sin-axcos-bxdx-if-a-b-and-use-it-to-0-n-sin-3xcos-2xdx-3-3-5-

Question Number 76965 by peter frank last updated on 02/Jan/20

E v a l u a t e

I_{a b} = \int \sin a x \cos b x d x

i f a \neq b a n d u s e i t t o

\int_{0}^{n} \sin 3 x \cos 2 x d x = \frac{3 - \sqrt{3}}{5}

Answered by mr W last updated on 01/Jan/20

\sin (a x + b x) = \sin a x \cos b x + \cos a x \sin b x

\sin (a x - b x) = \sin a x \cos b x - \cos a x \sin b x

\Rightarrow \sin a x \cos b x = \frac{\sin (a + b) x + \sin (a - b) x}{2}

I = \int \sin a x \cos b x d x

= \frac{1}{2} \int (\sin (a + b) x + \sin (a - b) x) d x

= - \frac{1}{2} [\frac{\cos (a + b) x}{a + b} + \frac{\cos (a - b) x}{a - b}] + C

Commented by peter frank last updated on 02/Jan/20

t h a n k y o u

Commented by peter frank last updated on 02/Jan/20

h o w a b o u t p a r t b

Commented by mr W last updated on 02/Jan/20

i t h i n k y o u s h o u l d b e a b l e t o d o

p a r t b b y y o u r s e l f . b u t i c a n n o t,

b e c a u s e i {d o n}^{'} t k n o w w h a t i s n i n

y o u r q u e s t i o n \int_{0}^{n} .

Commented by peter frank last updated on 02/Jan/20

t h a n k y o u