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MathSofiya
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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
\[\int_0^{\pi}(cost\hat i +sint\hat jt\hat k)\cdot(\hat i+cos(t) \hat j sint \hat k)dt\]
\[\int_0^{\pi}(cost+sintcost+tsint)dt\]
\[\int_0^{\pi} cost dt+\int_0^{\pi} sintcostdt+\int_0^{\pi}tsintdt\]
 one year ago
 one year ago
MathSofiya Group Title
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 \[\int_0^{\pi}(cost\hat i +sint\hat jt\hat k)\cdot(\hat i+cos(t) \hat j sint \hat k)dt\] \[\int_0^{\pi}(cost+sintcost+tsint)dt\] \[\int_0^{\pi} cost dt+\int_0^{\pi} sintcostdt+\int_0^{\pi}tsintdt\]
 one year ago
 one year ago

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MathSofiya Group TitleBest ResponseYou've already chosen the best response.1
\[sint]_0^{\pi}+\int_0^0 udu+[tcost+sint]_0^{\pi}\]
 one year ago

mukushla Group TitleBest ResponseYou've already chosen the best response.1
mukushla is not typing a reply…whats wrong with site...lol let me check it
 one year ago

MathSofiya Group TitleBest ResponseYou've already chosen the best response.1
LOL...i think mukushla should type a reply
 one year ago

mukushla Group TitleBest ResponseYou've already chosen the best response.1
its allright but what is that middle integral !!?
 one year ago

MathSofiya Group TitleBest ResponseYou've already chosen the best response.1
u substitution u =sint du=cost dt sin(pi)=0 sin(0)=0
 one year ago

mukushla Group TitleBest ResponseYou've already chosen the best response.1
almost done
 one year ago

MathSofiya Group TitleBest ResponseYou've already chosen the best response.1
cos Pi is 1 though
 one year ago

MathSofiya Group TitleBest ResponseYou've already chosen the best response.1
so negative pi should be the answer?
 one year ago

MathSofiya Group TitleBest ResponseYou've already chosen the best response.1
and cos (0) is 1 oh it cancels out!
 one year ago

MathSofiya Group TitleBest ResponseYou've already chosen the best response.1
no that still doesn't seem right... :(
 one year ago

mukushla Group TitleBest ResponseYou've already chosen the best response.1
i meant 0 for middle integral
 one year ago

mukushla Group TitleBest ResponseYou've already chosen the best response.1
answer is \(\pi\) ?
 one year ago

MathSofiya Group TitleBest ResponseYou've already chosen the best response.1
the first integral would be zero too and then we have left \[[tcost+sint]_0^{\pi}=\pi\]
 one year ago

mukushla Group TitleBest ResponseYou've already chosen the best response.1
We are DONE.....;D
 one year ago
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