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how to integrate
e^(2s) *Cos (s)/(4) , please help, I have no idea what to do, I would appreciate if you show your work with steps.

1 Answer

14 votes

Answer:


\int\limits {e^(2s) cos(s)/(4) ds =
(4 e^(2s) )/(65 ) ({8 cos ((1)/(4) ) s + sin (1)/(4) s} ))

Explanation:

Step(i):-

Given that
f(s) = e^(2s) cos(s)/(4)

Now integrating


\int\limits {f(s)} \, ds = \int\limits {e^(2s) cos(s)/(4) ds

By using integration formula


\int\limits { e^(ax) cos b x dx = (e^(ax) )/(a^(2)+b^(2) ) ( a cos b x + b sin b x )

Step(ii):-


\int\limits {e^(2s) cos(s)/(4) ds =
(e^(2s) )/((2)^(2)+((1)/(4)) ^(2) ) ( 2 cos ((1)/(4) ) s + (1)/(4) sin (1)/(4) s ))

=
(e^(2s) )/((4+(1)/(16))) ( 2 cos ((1)/(4) ) s + (1)/(4) sin (1)/(4) s ))

=
(e^(2s) )/(((65)/(16) ) ( (8 cos ((1)/(4) ) s + sin (1)/(4) s)/(4) ))

=
16 X(e^(2s) )/(65 ) ( (8 cos ((1)/(4) ) s + sin (1)/(4) s)/(4) ))

=
(4 e^(2s) )/(65 ) ({8 cos ((1)/(4) ) s + sin (1)/(4) s} ))

Final answer:-


\int\limits {e^(2s) cos(s)/(4) ds =
(4 e^(2s) )/(65 ) ({8 cos ((1)/(4) ) s + sin (1)/(4) s} ))

User BCran
by
7.8k points

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