Evaluate the integral

Question

anonymous · Answer

attachment

anonymous · Answer

My answer was marked incorrect but I'm not sure what i did wrong ?

yttrium · Answer

What method did you used?

anonymous · Answer

First thing I see of the bad is the variable? Should it have been t?

anonymous · Answer

u substitution!

anonymous · Answer

ohhh myy! I think that may be the reason why its incorrect?

abb0t · Answer

Yes, u-sub for the $\sf \color{}{x^2+5}$

abb0t · Answer

Err, i mean $t$*

anonymous · Answer

Well, ok but first things first does any one know if my answer is completely wrong or may it just be that i put the incorrect variable?

anonymous · Answer

i think it's just the variable at first glance

abb0t · Answer

Try sticking with the same variable. Your answer does look right tho..

anonymous · Answer

You guys were right!

anonymous · Answer

Didn't even notice -_-

anonymous · Answer

ONE MORE THING! if its possible can you guys help explain what i did wrong in this problem:

anonymous · Answer

attachment

anonymous · Answer

I worked it out a couple times and i kept getting the same answer as the one i typed but its incorrect apparently.

abb0t · Answer

$\sf \color{}{cos(\frac{\pi}{3})}$ is your problem.

anonymous · Answer

How so? :/

yttrium · Answer

should be negative cos

anonymous · Answer

yes well as my integral i got
-19cosx+x

abb0t · Answer

$$\int\limits dy = 19\int\limits \sin(t)+1~dt \Rightarrow ?$$

anonymous · Answer

then i plugged in pi/3 & set whole equation equal to 1/2

abb0t · Answer

Yes, so you get 19$\frac{1}{2}$ + $\frac{\pi}{3}$...

anonymous · Answer

yes! @abb0t i got that

abb0t · Answer

But you still have to solve for C.

anonymous · Answer

I did and thats how i arrived to my answer -pi/3+10?

abb0t · Answer

$\frac{1}{2}$=$\frac{19}{2}$+$\frac{\pi}{3}$+C

yttrium · Answer

Ooops. Isn't it that the answer here should be and equation as well?

anonymous · Answer

im not sure @Yttrium :/ 
@abb0t  thats what i had written down!

anonymous · Answer

well wait shouldn't it be -19/2?

abb0t · Answer

$-\frac{19}{2}$* sorry

yttrium · Answer

Yeah it should be.

anonymous · Answer

yes yes thought so :) @abb0t

abb0t · Answer

So, it should be $\sf \color{}{\frac{30- \pi}{3}}$=C

anonymous · Answer

hm did you just make it so it has a common denominator?

abb0t · Answer

Yes. Now plug in your C into the final equation, and thats your answer.

anonymous · Answer

so my final answer would be $$-19cosx+x+\frac{ 30-\pi }{ 3 }$$

anonymous · Answer

??? @abb0t

zarkon · Answer

t

abb0t · Answer

Yes, in terms of t.