Question

Here is my last question for tonight. Not sure I'm going to get it done on time for the assignment, but I still need to do it. Here is the problem: https://gyazo.com/514a439399ea0f00a3c37c617acedbc0
Let me know if there is any issues with the screenshot.

Answer 1

(a)

u = f(x)
du/dx = f ' (x)
du = f ' (x) * dx

look at the limits of integration for the given integral (not the answer choices)

if x = 0, then u = f(x) = f(0) = ???
use the table and tell me what f(0) is equal to

Answer 2

f(0) is 5, right? and f(1) would be 8?

Answer 3

yep, so \[\Large \int_{\color{red}{0}}^{\color{blue}{1}}f \ '(x)\sin(f(x))dx = \int_{\color{red}{5}}^{\color{blue}{8}}\sin(u)du\]

Answer 4

Then... taking the integral would result in \[-\cos(8) - -\cos(5)\] but I need an exact value. Or does that count as one in itself? I can't check my answer anymore since I ran out of time, but it's fine, I'll just keep going until I finish it anyway.

Answer 5

which simplifies to `cos(5) - cos(8)`

Answer 6

`cos(5) - cos(8)` is the exact value because there isn't any simple radical expression to replace the cosines with