Evaluating definite integrals?

Question

find the general indefinite integral. illustrate by graphing several members of the family on the same screen.

∫ (cos(x)-2sin(x)) dx

what does it mean by family members could you please give me an example of one

Answer 1

sin x - 2 cos x + K

Different family members will be obtained by allocating different values to K

Answer 2

∫ (cos(x)-2sin(x)) dx

= ∫ cos(x) dx - 2∫ sin(x) dx

= sin(x) - 2(-cos(x)) + C

= sin(x) + 2cos(x) + C

Remember that every time you integrate you get a constant.  You could let C = 1 or C = 3 or C = 4.56.  In other words you can have tons of different C's.  Therefore, by graphing many different expressions with different values of C you'll get a family of curves and each one of these curves is called a member of the family of curves.

Hope this helps!

@como:  I never understand people like you.  I've given the question a good answer already, why do you bother answering?  Are you that desperate for points?  

No wonder you have over 100,000 points.  I checked your profile and you did the same thing with another question and that one happened to be answered by 3 other TC's.  You have my thumbs down.