Question

calc 2

Answer 1

First of all, I notice that F'(t) can easily be integrated (which produces a constant of integration, C). It may be easiest to simply perform this integration, find C, and then evaluate F(t) for each of the given t values.

Answer 2

You could paraphrase that to "evaluate F(b) for each of the given b values."

Answer 3

Tachi: please integrate:\[\int\limits_{}^{}\sin t \cos t dt\]

Answer 4

Hint: use a simple substitution.

Answer 5

i can't see the equation. can you post in a pic?

Answer 6

let u=... Simple u sub.

Answer 7

I'd love to post a pic, but the Draw utility is not currently functioning.
Go ahead, raffle_snaffle: propose the actual substitution you have in mind.

Answer 8

Sry, I'm not sure what to do. We haven't gotten to U substitution yet

Answer 9

use advanced guessing

Answer 10

before that simplify, sint cost to 1/2 sin(2t)

Answer 11

we knw that derivative of -cos is sin.
having known that, clearly the integral of sin(2t) will have a -cos(2t) term.

Answer 12

next, fix it be thinking a bit more.. :

does derivative of -cos(2t) give u sin(2t) ?
no, it gives u sin(2t) * 2,
so u need to divide by 2

Answer 13

overall :

integral sin t cos t dt

integral 1/2 sin(2t) dt

1/2 integral sin(2t) dt

1/2 [-cos(2t)]/2 + C

-1/4 cos(2t) + C

Answer 14

plugin the given point, and find C

Answer 15

Plug in 13?

Answer 16

@ganeshie8

Answer 17

we got F(t) = -1/4cos(2t) + C

Answer 18

and we're given F(0) = 13

Answer 19

plugin t = 0 :)

Answer 20

C = 13.25?

Answer 21

yes !

Answer 22

cool, where to go from there?

Answer 23

F(t) = -1/4cos(2t) + 13.25

F(b) = -1/4cos(2b) + 13.25

Answer 24

we're done wid calculus part,
rest is just algebra

Answer 25

compute the function values

Answer 26

F(b) = -1/4cos(2b) + 13.25

F(0) = ?

Answer 27

13

Answer 28

simply evaluate other values also

Answer 29

ok cool

Answer 30

Thank you. got em

Answer 31

np :)