Question

Assume f(x) and g(x) are differentiable on [1,4]. If f(1)=2, g(1)=-3, f(4)=5, g(4)=0, and Integral[g(x)f'(x),x,1,4]=1, find Integral[f(x)g'(x),x,1,4]
A.-7
B. -1
C. 5

I got C, can anyone check my work?

Answer 1

cant really make out the querstion

Answer 2

\[\int\limits_{1}^{4}g(x)f'(x) =1\]
\[\int\limits_{1}^{4}f(x)g'(x) =?\]

Answer 3

given that f(1)=2, g(1)=-3, f(4)=5, g(4)=0

Answer 4

integrate by parts

Answer 5

Int = [f(x)g(x)] from 4 to 1
- f'(x)g(x)dx from 1 to 4

Answer 6

get it?

Answer 7

thats f(4)g(4) - f(1)g(1) - 1

Answer 8

get it>?????

Answer 9

6-1 = 5

Answer 10

okay, so you got 5 as well?

Answer 11

thats the answer mate

Answer 12

thanks!

Answer 13

no prob