Question

Intigrate (sin 2x + cos 2x)dx=1/2sin(2x-c)+a

Answer 1

a = 135° b = C

Step-by-step explanation:

∫(sin2x-cos2x)dx = (1/√2)sin(2x-a) + b

∫ sin2xdx - ∫cos2xdx = (1/√2)sin(2x-a) + b

 - cos2x/2-sin2x/2 + C= sin2xcosa/√2 - cos2xsina/2 +b

 Compare coefficients of sin2x cos2x and constant

sin2xcosa/√2 =  - sin2x/2

- cos2xsina/2 = - cos2x/2

we get

-1/2=cosa/√2 so, cosa= -1/√2

 -1/2=- - sina/√2  So , sina= 1/√2

 Sin is Positive and cos is negative means a is in II quadrant

Hence a = 90+45+135

 and b = C . any constant