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Evaluate $\int_0^\infty\frac{dx}{(x^2 + a^2)^3}dx$, using contour integration.
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
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Evaluate $\int_{-\infty}^{\infty} \frac{x^2 + x + 2}{x^4 + 10x^2 + 9}dx$, using contour integration.
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
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Evaluate $\int_{- \infty}^{\infty} \frac{x^2}{(x^2+a^2)(x^2+b^2)}dx$, a>0, b>0 using contour integration.
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
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Evaluate $\int_0^{\pi} \frac{d \theta}{3+2 cos \theta}$
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
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Evaluate $\int_0^{2 \pi} \frac{cos 2 \theta}{5+4 cos \theta} d \theta$
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
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Evaluate $\int_0^{2\pi} \frac{d \theta}{5+3 sin \theta}$
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
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8.2k
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Evaluate $\int \frac{e^z}{z^2+ \pi^2}dz$ where C is |z|=4 ,using residue theorem
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
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Evaluate $\int \frac{z^2}{(z-1)^2(z+1)}dz$ where C is |z| = 2, using residue theorem.
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
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Find the residues of $f(z) = \frac{sin \pi z^2 + cos \pi z^2}{(z - 1)(z - 2)^2}$ at its pole.
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
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Obtain Tayiors & Laurents series expansions of function $f(z) = \frac{z-1}{z^2-2z-3}$ indicating regions of convergence.
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
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Find Laurents series which represent the function
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
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Obtain all Tayiors & Laurents series expansions of function $\frac{(z-2)(z+2)}{(z+1)(z+4)}$ about z = 0
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
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If $f(a)= \int \frac{4z^2 + z +5}{z - a}dz$, where C is the circle $|z| = 2$, find the values of f(1), f(i), $f''(-i)$.
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
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If C is the circle $|z|=1$, using the integral $\int \frac{e^{kz}}{z}dz$, where K is real, show that $\int_0^{\pi} e^{k cos \theta} cos (ksin \theta) d \theta = \pi$
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
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Using Cauchys integral formula ,evaluate $\oint \frac{12z-7}{(z-1)^2(2z+3)}dz$, where c is the circle $|z+i| = \sqrt{3}$
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
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5.8k
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$\oint \frac{dz}{z^3(z+4)}$ ,where c is the circle |z|=2.
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
6
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16k
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Evaluate the integral $\int_0^{1+i}(x^2 - iy)dz$ along the path y = x.
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
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12k
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Evaluate the integral $\int_0^{1+i}(x - y + ix^2)dz$, along the line from z = 0 to z = 1 + i.
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
4
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23k
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Evaluate $\oint(z - z^2)dz$ Where C is the upper half of the circle |z|=1.What is the value of the integral for the upper half of the same circle.
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
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1.5k
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Evaluate $\oint(\bar{z} +2z)dz$, Where C is the unit circle in the Z plane.
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
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1
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7.5k
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Show that $\oint log z dz = 2 \pi i$,Where C is the unit circle in the Z plane.
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
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1.9k
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Evaluate $\int \int \int (x + y + z) dx \ dy \ dz$ over the tetrahedron bounded by the planes x = 0, y = 0, z = 0 and x + y + z = 1
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
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838
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Evaluate $\int\int\int \sqrt{1 - \frac{x^2}{a^2} - \frac{y^2}{b^2} - \frac{z^2}{c^2}}$ dx dy dz over the ellipsoid $\frac{x^2}{a^2} + \frac{y^2}{b^2} + \frac{z^2}{c^2} = 1$
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
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Find the volume of the paraboloid $x^2 + y^2 = 4z$ cut off by the plane z = 4
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
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Evaluate $\int\int\int_v x^2 dx \ dy \ dz$ over the volume bounded by the planes $x = 0, y = 0, z = 0 \ and \frac{x}{a} + \frac{y}{b} + \frac{z}{c} = 1$
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
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