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Complex integrals to be evaluated using the residue theorem. The integrals involve functions with exponentials, sines, and cosines. The integral expression, the limits of integration, and the possible answers in multiple-choice format.
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Using Residue theorem or otherwise evaluate following integrals:
−∞
x^2 (x^2 + 1)(x^2 + 9)
d x equals
(A) π 2
(B) π 4
(C) π 6
(D) π 8
(E) none of the above
−∞
x^2 − x + 2 x^4 + 10x^2 + 9
d x equals
(A) 53 π
(B) 56 π
(C) 512 π
(D) 415 π
(E) none of the above
−π
13 + 12 sin(θ)
d θ equals
(A) π 2
(B) 25 π
(C) 23 π
(D) 27 π
(E) none of the above
−∞
(x − 1) eix x^2 − 2 x + 2
d x equals
(A) π i e−1+i (B)π i ei^ −^2 (C) π i e2 i^ −^1 (D) −π i (E) none of the above
−∞
(x − 3) ei^ x x^2 − 6 x + 109
d x equals
(A) π(1 − i) e−3 i^ −^6 (B)π i e3 i^ −^10 (C) 2π (D) −π i (E) none of the above
−∞
(x + 1) e−3 i^ x x^2 − 2 x + 5
d x equals
(A) π(1 − i) e−3 i^ −^6 (B)π i e3 i^ −^10 (C) π i (D) −π i (E) none of the above
−∞
(x + 1) sin(2x) x^2 + 2x + 2
d x equals
(B) π e−^2 sin(2) (C) 2π e−^2 sin(2) (D) π e−^2 cos(2) (E) 2π e−^2 cos(2)
−∞
x sin(x) x^2 + 2x + 10
d x equals
