Some please teach me how to do this test in a few hours and the book doesn't help!?!

Question

anonymous · Answer

attachment

anonymous · Answer

i know how to get the derivative I just have no clue how to get the (-\pi +2)

ganeshie8 · Answer

after integrating, wat did u get ?

anonymous · Answer

-4	heta+tan	heta

ganeshie8 · Answer

thats wrong.

anonymous · Answer

i know, i have no clue

ganeshie8 · Answer

where is ur integration constant ?

ganeshie8 · Answer

whenever u take indefinite integral, the constant pops up aswell

anonymous · Answer

oh you're talking about the +C yes i know that is what is missing but have no clue how to find it

ganeshie8 · Answer

$\large  r'(\theta) = -4 + \sec^2 \theta$

$\large  r(\theta) =  \int -4 + \sec^2 \theta   d\theta$

$\large  r(\theta) =  -4\theta  + \tan \theta   + C$

anonymous · Answer

right i can get that far exactly lol.. how do i get the C

ganeshie8 · Answer

we're given that $\large  \left(-\frac{\pi}{4}, 1\right)$ is a point on $\large r(\theta)$  right ?

anonymous · Answer

yes plugging in -(\pi)/4 gives me 1 though

ganeshie8 · Answer

plug $\large   r = 1,  \theta =   -\frac{\pi}{4}$  in the above equation and solve $\large C$

ganeshie8 · Answer

$\large  r(\theta) =  -4\theta  + \tan \theta   + C$


$\large  1  =  -4(-\frac{\pi}{4})  + \tan (-\frac{\pi}{4})   + C$

ganeshie8 · Answer

$\large  1  =  \pi    -1   + C$


$\large   C =  2 -  \pi$

anonymous · Answer

thank you very much... very easy once i understood it, just learned this C thing last couple weeks

ganeshie8 · Answer

np :) wish u good luck wid d test !!

anonymous · Answer

thank you