Question

Find f.
f ''(t) = 7et + 9 sin t, f(0) = 0, f(π) = 0

Answer 1

7e^t

Answer 2

ok then start with integrating

Answer 3

yeah im having trouble with the last step

Answer 4

plugging in pi

Answer 5

ok i,m doing it verify it ok?

Answer 6

okay

Answer 7

f(t) = 7e^t-9sint+Ct+D

Answer 8

\[f''(t)=7e^t+9sint\\f'(t)=7e^t-9cost+c\]
now find f'(0)

Answer 9

its f(0) so we dont plug it in yet until we integrate it one more time right?

Answer 10

\[f(t) = 7e^t-9\sin t+C t +D\]

so you plug in f(0)=0 ... what do you get for D

Answer 11

-7

Answer 12

now put D=-7
and f(pi)=0

Answer 13

\[f(t) = 7e^t-9\sin t+C t -7\]

and plugging \(f(\pi)=0\) ...

Answer 14

-((7e^pi)/pi) +7

Answer 15

\[0 =7e^\pi+\pi C -7\]

\[\large \implies C= {7-7e^\pi \over \pi}\]

Answer 16

thank you!