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trigonometric integration

question: ∫ [2sin2xsin5x]dx.

given that cos(3x)-cos(7x) = cos(-3x)-cos(7x)

does ∫ [cos(3x)-cos(7x)]dx= ∫ [cos(-3x)-cos(7x)]dx.

i am just wondering because the textbook says the correct answer is ∫ [cos(3x)-cos(7x)]dx and i got ∫ [cos(-3x)-cos(7x)]dx.

Reply 1

Kevin De Bruyne

Remember the rules... sin(-x) = -sin(x) and cos(-x) =...?

If it helps, draw cos(-x) and cos(x).

Reply 2

lukejoshjames

Look at a graph of Cos(x) and you'll see that Cos(-x)=Cos(x), so don't worry you're still correct.

Reply 3

WhiteGroupMaths

Just remember the Cosine function is a greedy animal; it digests any minus sign present internally. Sine and Tangent functions will spit the minus sign out, ie sin(-x) =-sin x and tan(-x)= -tan x

Peace.

(edited 8 years ago)