Question

If u = ſe^ax cos bx dx and v= ſe^ax sin bx dx, then (a^2 + b^2 )(u^2 + v^2 ) =
(A) 2e^ax
(B) (a^2 + b^2 )e^2ax
(C) e^2ax
(D) (a^2 - b^2 )e^2 ax​

Answer 1

Step-by-step explanation:

u=e^ax-sinbx+cosbxe^axa

v=e^axcosbx+sinbxe^axa

u=-e^axsinbx+e^axcosbx

u=e^ax(-sinbx+cosbx)

v=e^ax(cosbx+sinbx)

u^2=e^2ax(cos^2bx-2sinbxcosbx+sin2bx)

u^2=e^2ax(1-2sinbxcosbx)

v^2=e^2ax(1+2sinbxcosbx)

u^2+v^2=2e^2ax

(a^2+b^2)2e^2ax

answer=B