A community for students.
Here's the question you clicked on:
 0 viewing
MathSofiya
 2 years ago
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:
\[\hat r(t)=\hat i +cost \hat j sint \hat k\]
\[F(x, y, z)=z\hat i+y \hat jx\hat k\]
x=t y=sint z=cost
\[\int_0^{\pi}(cost\hat i +sint\hat jt\hat k)\cdot(\hat i+cos(t) \hat j sint \hat k)dt\]
\[\int_0^{\pi}(cost+sintcost+tsint)dt\]
\[\int_0^{\pi} cost dt+\int_0^{\pi} sintcostdt+\int_0^{\pi}tsintdt\]
MathSofiya
 2 years ago
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: \[\hat r(t)=\hat i +cost \hat j sint \hat k\] \[F(x, y, z)=z\hat i+y \hat jx\hat k\] x=t y=sint z=cost \[\int_0^{\pi}(cost\hat i +sint\hat jt\hat k)\cdot(\hat i+cos(t) \hat j sint \hat k)dt\] \[\int_0^{\pi}(cost+sintcost+tsint)dt\] \[\int_0^{\pi} cost dt+\int_0^{\pi} sintcostdt+\int_0^{\pi}tsintdt\]

This Question is Closed

MathSofiya
 2 years ago
Best ResponseYou've already chosen the best response.1\[sint]_0^{\pi}+\int_0^0 udu+[tcost+sint]_0^{\pi}\]

mukushla
 2 years ago
Best ResponseYou've already chosen the best response.1mukushla is not typing a reply…whats wrong with site...lol let me check it

MathSofiya
 2 years ago
Best ResponseYou've already chosen the best response.1LOL...i think mukushla should type a reply

mukushla
 2 years ago
Best ResponseYou've already chosen the best response.1its allright but what is that middle integral !!?

MathSofiya
 2 years ago
Best ResponseYou've already chosen the best response.1u substitution u =sint du=cost dt sin(pi)=0 sin(0)=0

MathSofiya
 2 years ago
Best ResponseYou've already chosen the best response.1so negative pi should be the answer?

MathSofiya
 2 years ago
Best ResponseYou've already chosen the best response.1and cos (0) is 1 oh it cancels out!

MathSofiya
 2 years ago
Best ResponseYou've already chosen the best response.1no that still doesn't seem right... :(

mukushla
 2 years ago
Best ResponseYou've already chosen the best response.1i meant 0 for middle integral

MathSofiya
 2 years ago
Best ResponseYou've already chosen the best response.1the first integral would be zero too and then we have left \[[tcost+sint]_0^{\pi}=\pi\]
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.