Question

Evaluate the indefinite integral

Answer 1

Remember that cos theta is an even function

Answer 2

\[\cos(- \theta) = \cos(\theta)\]

Answer 3

Don't be afraid of theta, it's the same if it said x

Answer 4

so how would we o this haha

Answer 5

its not theta squared/2 right?

Answer 6

right

Answer 7

So our integral is \[\int\limits (\theta - \cos(\theta)) d \theta = \int\limits \theta d \theta - \int\limits \cos (\theta) d \theta \]

Answer 8

ok i see what you did there

Answer 9

whats the anti of theta?

Answer 10

\[\int\limits x dx = x^2/2\]

Answer 11

That's your hint but me saying hint didn't show up haha

Answer 12

lol so is it theta squared/2 - sintheta

Answer 13

+C

Answer 14

also i dont understand why u made cos theta positive ?

Answer 15

Because as I stated cos theta is an even function remember even functions f(-x) = f(x)

Answer 16

i apologize but is sin also even? What makes a functions even agin?

Answer 17

Nope, sin is odd :P

Answer 18

f(-x) = -f(x) for odd

Answer 19

what differentiates even and odd?

Answer 20

ok that makes sense

Answer 21

but aren't they both symmetric over the yaxis?

Answer 22

Not exactly, I think you may find this of interest: https://www.mathsisfun.com/algebra/functions-odd-even.html

Answer 23

thanks! so final answer is theta squared/2 - sintheta

Answer 24

+C

Answer 25

haha thats cause its indefinite right?

Answer 26

Correct

Answer 27

would the asnwer have changed if i left it as sin(-theta)

Answer 28

thats my last question btw. I appreciate all your support!

Answer 29

Yes, you would have theta `+` sin theta then

Answer 30

ok so I guess I should learn to recognize that. Appreicate the help!

Answer 31

THeres no other even functions that are tigonometric idetnities rght

Answer 32

i'm just gonna memorize cosine as even lol

Answer 33

Oh haha, secx is also even

Answer 34

The other four are odd however