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

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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 \[[tcost+sint]_0^{\pi}=\pi\]
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