Question

let f be twice differentiable with f(0)=6, f(1)=5, and f'(1)=2. Evaluate the integral (x(f^n)x dx) from 0 to 1

Answer 1

\[\int\limits xf^{n}(x)dx\]???

Answer 2

you forgot the bounds :)

Answer 3

\[\int^{1}_{0}x\ f''(x)\ dx\]

Answer 4

\(x\ f'(x) -f(x)\) if we do ibps

Answer 5

\[x\ f'(x) -f(x)-(x\ f'(x) -f(x))\]
\[1\ f'(1) -f(1)-(0\ f'(0) -f(0))\]
\[1\ (2) -5-(0\ f'(0) -6)\]
\[2-5+6=3\]

Answer 6

thats my story and im sticking to it :)

Answer 7

is actually f to the power of n

Answer 8

how do you get the integral distribute