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HOW TO INTEGRATE sin(ax+b) cos(ax+b)dx

HOW TO INTEGRATE   sin(ax+b) cos(ax+b)dx

Grade:12th pass

2 Answers

Godfrey Classic Prince
633 Points
11 years ago

Dear ABHISHEK VASHIST,

To integrate sin(ax+b) cos(ax+b),follwo these steps

let ax+b=t

then dx=dt/a

the expression is transformed to 

1/a*(sin 2t).dt

integrating it we get

1/a*(-1/2)*(cos 2t) +c

 

Hope this helped you immensely...

All the Very Best & Good Luck to you ...

Regards,

AskIITians Expert,

Godfrey Classic Prince

IIT-Madras

Please approve my answer if you liked it by clicking on "Yes" given below...!!Smile

basit ali
41 Points
11 years ago

for this apply fllowing sobstitution:i.e double substitution:

let, ax+b= t 

then adx=dt

then,dx=dt/a

then,∫sin(t)cos(t)dt/a......1 

then,1/a∫sin t cos t dt

now, cos(t)=z (suppose)

then, dcos (t)/dt= dz/dt

or,  -sint = dz then substituting the value  in 1,

we get ,-1/a ∫dz.z then by integrating, we get -z2/2a, now by putting the value we get, -cos(t)2/2a= -cos(ax+b)2/2a. if you like my answer plz approve!!!CoolSmileSmileCoolCoolCool

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