Thread: help with intergration by recogbition

G(x)=(10-x)cos((pi)x)
find an expression for the derivative G'(x)
i got that but then it says
hence show that an antiderivative of f(x) is
F(x)= ((sin((pi)x)) \ (pi)) - G(x)

and f(x) =pi(10-x)sn(pi)x

Originally Posted by dustinbehemoth

G(x)=(10-x)cos((pi)x)
find an expression for the derivative G'(x)
i got that but then it says
hence show that an antiderivative of f(x) is
F(x)= ((sin((pi)x)) \ (pi)) - G(x)

and f(x) =pi(10-x)sn(pi)x

What do you get for the derivative?

the derivative of g(x) was
(pi)(10-x)sin(pi)x - cos(pi)x

Originally Posted by dustinbehemoth

the derivative of g(x) was
(pi)(10-x)sin(pi)x - cos(pi)x

Let .... (1)

Then .... (2)

Integrate both sides of (2) with respect to x:

.

Substitute from (1):

.

Make the required integral the subject etc.

found a heaps easier(may just be better explained) way but thanks anyway