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

mukushlaBest 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

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

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

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

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

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

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

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

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

MathSofiyaBest 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
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