Question

Integrate (sinxcosx) dx

Answer 1

might want to consider what the derivative of sin or cos is ...

Answer 2

hmm i did substitution but i got 2 separate answers, one is 1/2sin2x and the other is -1/2cos^2x

Answer 3

* 1/2sin^2x

Answer 4

sin^n (x) derives to n sin^(n-1)(x) cos(x) right?

Answer 5

1/2 sin^2(x) seems appropriate to me

Answer 6

i'd say both are correct but incomplete.
1/2 sin^2 x + c
is equivalent to
-1/2 cos^2x +c

Answer 7

i was leading to that as well :)

Answer 8

you can always use the identity
sin^2 x + cos^2 x =1
to interchange among those 2 equivalent forms

Answer 9

the constant you get 1/2 or -1/2 can be combined with the constant c to get another constant say C

Answer 10

did your doubt get cleared ?

Answer 11

hm i think so, then the answers are both correct, but there must be a c there which are equal to each other?

Answer 12

the 'c' there is just to represent the constant of integration
like x^2+c and x^2+1+c are equivalent functions, because the derivative of both of them is 2x

so, yes, you can say both are correct, but with different constant "c" values, which does not matter

Answer 13

i see, okay that makes it clear now, thanks! :D

Answer 14

welcome ^_^