Question

Evaluate the line integral \[\int_c F\cdot dr\]
where c is given by
\[\hat r (t)=t\hat i +sint\hat j +cost \hat k\]
\[0 \le t le \pi\]
and:
\[\hat r(t)=\hat i +cost \hat j -sint \hat k\]
\[F(x, y, z)=z\hat i+y \hat j-x\hat k\]
x=t y=sint z=cost
\[\int_0^{\pi}(cost\hat i +sint\hat j-t\hat k)\cdot(\hat i+cos(t) \hat j -sint \hat k)dt\]
\[\int_0^{\pi}(cost+sintcost+tsint)dt\]
\[\int_0^{\pi} cost dt+\int_0^{\pi} sintcostdt+\int_0^{\pi}tsintdt\]

Answer 1

\[sint]_0^{\pi}+\int_0^0 udu+[-tcost+sint]_0^{\pi}\]

Answer 2

mukushla is not typing a reply…whats wrong with site...lol

let me check it

Answer 3

LOL...i think mukushla should type a reply

Answer 4

its allright but what is that middle integral !!?

Answer 5

u substitution
u =sint
du=cost dt
sin(pi)=0
sin(0)=0

Answer 6

almost done

Answer 7

0?

Answer 8

yes

Answer 9

cos Pi is -1 though

Answer 10

so negative pi should be the answer?

Answer 11

and cos (0) is 1 oh it cancels out!

Answer 12

no that still doesn't seem right... :(

Answer 13

i meant 0 for middle integral

Answer 14

answer is \(\pi\) ?

Answer 15

the first integral would be zero too
and then we have left
\[[-tcost+sint]_0^{\pi}=\pi\]

Answer 16

YAY!

Answer 17

We are DONE.....;-D