Calculate the path integral: $int_{lambda}left[2z+sinhleft(zright)right],mathrm{d}z$
Calculate the path integral:
$$int_{lambda}left[2z + sinhleft(zright)right],mathrm{d}z$$
where $displaystylelambdaleft(tright) =
frac{t^{2}}{4} + frac{mathrm{i}t}{2},,quad
left(~0 ≤ t ≤ 4~right)$.
Im not sure how to parameterize this and also how to answer the rest of the question so any help will be appreciated.
integration complex-analysis
edited Nov 24 at 19:09
Felix Marin
67k7107139
add a comment |
Calculate the path integral:
$$int_{lambda}left[2z + sinhleft(zright)right],mathrm{d}z$$
where $displaystylelambdaleft(tright) =
frac{t^{2}}{4} + frac{mathrm{i}t}{2},,quad
left(~0 ≤ t ≤ 4~right)$.
Im not sure how to parameterize this and also how to answer the rest of the question so any help will be appreciated.
integration complex-analysis
edited Nov 24 at 19:09
Felix Marin
67k7107139
3
Can't you just find the anti-derivative ?
– Zaid Alyafeai
Mar 20 '17 at 21:54
add a comment |
Calculate the path integral:
$$int_{lambda}left[2z + sinhleft(zright)right],mathrm{d}z$$
where $displaystylelambdaleft(tright) =
frac{t^{2}}{4} + frac{mathrm{i}t}{2},,quad
left(~0 ≤ t ≤ 4~right)$.
Im not sure how to parameterize this and also how to answer the rest of the question so any help will be appreciated.
integration complex-analysis
edited Nov 24 at 19:09
Felix Marin
67k7107139
Calculate the path integral:
$$int_{lambda}left[2z + sinhleft(zright)right],mathrm{d}z$$
where $displaystylelambdaleft(tright) =
frac{t^{2}}{4} + frac{mathrm{i}t}{2},,quad
left(~0 ≤ t ≤ 4~right)$.
Im not sure how to parameterize this and also how to answer the rest of the question so any help will be appreciated.
integration complex-analysis
integration complex-analysis
edited Nov 24 at 19:09
Felix Marin
67k7107139
edited Nov 24 at 19:09
Felix Marin
67k7107139
edited Nov 24 at 19:09
Felix Marin
67k7107139
edited Nov 24 at 19:09
Felix Marin
67k7107139
edited Nov 24 at 19:09
Felix Marin
67k7107139
67k7107139
asked Mar 20 '17 at 20:54
user387758
3
Can't you just find the anti-derivative ?
– Zaid Alyafeai
Mar 20 '17 at 21:54
add a comment |
3
Can't you just find the anti-derivative ?
– Zaid Alyafeai
Mar 20 '17 at 21:54
3
3
Can't you just find the anti-derivative ?
– Zaid Alyafeai
Mar 20 '17 at 21:54
Can't you just find the anti-derivative ?
– Zaid Alyafeai
Mar 20 '17 at 21:54
add a comment |
1 Answer
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Hint: Use the Fundamental Theorem of Calculus for contour integrals:
If $f$ is continuous on a domain $D$, then the integral along any path from $z_1$ to $z_2$ is given by
$$ int_{z_1}^{z_2} f(z) , dz = F(z_2) - F(z_1) $$
where $F$ is any antiderivative of $f$.
answered Mar 21 '17 at 21:06
WB-man
1,745417
add a comment |
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1 Answer
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oldest
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1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
Hint: Use the Fundamental Theorem of Calculus for contour integrals:
If $f$ is continuous on a domain $D$, then the integral along any path from $z_1$ to $z_2$ is given by
$$ int_{z_1}^{z_2} f(z) , dz = F(z_2) - F(z_1) $$
where $F$ is any antiderivative of $f$.
answered Mar 21 '17 at 21:06
WB-man
1,745417
add a comment |
Hint: Use the Fundamental Theorem of Calculus for contour integrals:
If $f$ is continuous on a domain $D$, then the integral along any path from $z_1$ to $z_2$ is given by
$$ int_{z_1}^{z_2} f(z) , dz = F(z_2) - F(z_1) $$
where $F$ is any antiderivative of $f$.
answered Mar 21 '17 at 21:06
WB-man
1,745417
add a comment |
Hint: Use the Fundamental Theorem of Calculus for contour integrals:
If $f$ is continuous on a domain $D$, then the integral along any path from $z_1$ to $z_2$ is given by
$$ int_{z_1}^{z_2} f(z) , dz = F(z_2) - F(z_1) $$
where $F$ is any antiderivative of $f$.
answered Mar 21 '17 at 21:06
WB-man
1,745417
Hint: Use the Fundamental Theorem of Calculus for contour integrals:
If $f$ is continuous on a domain $D$, then the integral along any path from $z_1$ to $z_2$ is given by
$$ int_{z_1}^{z_2} f(z) , dz = F(z_2) - F(z_1) $$
where $F$ is any antiderivative of $f$.
answered Mar 21 '17 at 21:06
WB-man
1,745417
answered Mar 21 '17 at 21:06
WB-man
1,745417
answered Mar 21 '17 at 21:06
WB-man
1,745417
answered Mar 21 '17 at 21:06
WB-man
1,745417
1,745417
add a comment |
add a comment |
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3
Can't you just find the anti-derivative ?
– Zaid Alyafeai
Mar 20 '17 at 21:54