Helping my brother with his calculus homework and I gave him the right answer, but I used my calculator to integrate something that he doesn't understand. He says he tried to do said integration by hand and got something different; I then integrated it by hand and got what he got. The equation:
(a = 0, b = t)[SIZE="4"]∫[/SIZE][k/(t+1)^2 (dt)] = -k/t+1
Could someone map that out for me? I know it's relatively simple but I can't seem to do the integration by hand. When I do, I get:
(a = 0, b = t)[SIZE="4"]∫[/SIZE][k/(t+1)^2 (dt)]
= [-k/(t+1)] - [-k/(0+1)]
= -k/(t+1) + k
Now, the problem with this: The original equation, k/(t+1)^2, = f'(t), meaning by my calculations -k/(t+1) + k = f(t). The problem that my brother needs help with involves calculating f(0), which = -k. But:
f(t) = -k/(t+1) + k
f(0) = -k/(0+1) + k
= -k + k
= 0
The correct solution:
f(t) = -k/(t+1)
f(0) = -k/(0+1)
= -k
I must be forgetting an integration law or something.
(a = 0, b = t)[SIZE="4"]∫[/SIZE][k/(t+1)^2 (dt)] = -k/t+1
Could someone map that out for me? I know it's relatively simple but I can't seem to do the integration by hand. When I do, I get:
(a = 0, b = t)[SIZE="4"]∫[/SIZE][k/(t+1)^2 (dt)]
= [-k/(t+1)] - [-k/(0+1)]
= -k/(t+1) + k
Now, the problem with this: The original equation, k/(t+1)^2, = f'(t), meaning by my calculations -k/(t+1) + k = f(t). The problem that my brother needs help with involves calculating f(0), which = -k. But:
f(t) = -k/(t+1) + k
f(0) = -k/(0+1) + k
= -k + k
= 0
The correct solution:
f(t) = -k/(t+1)
f(0) = -k/(0+1)
= -k
I must be forgetting an integration law or something.