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1. Âû÷èñëèòü íåñîáñòâåííûé èíòåãðàë
∞
−∞
ax2
+bx+c
fx4+gx3+hx2+jx+k dx, ãäå
Âàðèàíò 1=Âàðèàíò 4: (a, b, c, f, g, h, j, k) = (1, 2, 3, 1, 0, 2, 0, −3)
Âàðèàíò 2=Âàðèàíò 5: (a, b, c, f, g, h, j, k) = (−2, 6, 10, 2, 3, 4, 3, 2)
Âàðèàíò 3=Âàðèàíò 6: (a, b, c, f, g, h, j, k) = (4, −3, 1, 2, 0, 10, 0, −8)
Âàðèàíò 4=Âàðèàíò 8: (a, b, c, f, g, h, j, k) = (3, 2, 1, 2, −3, −5, −3, 2)
2. Âû÷èñëèòü íåñîáñòâåííûé èíòåãðàë
∞
−∞
δ0
aeibx
+δ0
c sin(fx)
gx3+hx2+jx+k dx, ãäå
Âàðèàíò 1=Âàðèàíò 4: (a, b, c, f, g, h, j, k) = (0, 2, 1, 7, 1, 4, 4, 1)
Âàðèàíò 2=Âàðèàíò 5: (a, b, c, f, g, h, j, k) = (1, 9, 0, 3, 0, 2, 3, 4)
Âàðèàíò 3=Âàðèàíò 6: (a, b, c, f, g, h, j, k) = (0, −1, 1, 10, 2, 5, 5, 2)
Âàðèàíò 4=Âàðèàíò 8: (a, b, c, f, g, h, j, k) = (1, −3, 0, −4, 0, 4, 2, 6)
3. Âû÷èñëèòü íåñîáñòâåííûé èíòåãðàë
∞
−∞
eax
ebx+c
dx, ãäå
Âàðèàíò 1=Âàðèàíò 4: (a, b, c) = (1 + i, 2, 1)
Âàðèàíò 2=Âàðèàíò 5: (a, b, c) = (3 − i, 4, 10)
Âàðèàíò 3=Âàðèàíò 6: (a, b, c) = (−1 + 2i, −5, −1)
Âàðèàíò 4=Âàðèàíò 8: (a, b, c) = (−1 − 3i, −3, −2)
4. Âû÷èñëèòü íåñîáñòâåííûé èíòåãðàë
∞
a
1
(bx2+cx+f)·
√
x−a
dx, ãäå
Âàðèàíò 1=Âàðèàíò 4: (a, b, c, f) = (1, 1, 3, 6)
Âàðèàíò 2=Âàðèàíò 5: (a, b, c, f) = (−1, 2, 4, 5)
Âàðèàíò 3=Âàðèàíò 6: (a, b, c, f) = (0, 1, i, 5)
Âàðèàíò 4=Âàðèàíò 8: (a, b, c, f) = (0, 2, −i, 3)
1

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залікове інтеграли

  • 1. 1. Âû÷èñëèòü íåñîáñòâåííûé èíòåãðàë ∞ −∞ ax2 +bx+c fx4+gx3+hx2+jx+k dx, ãäå Âàðèàíò 1=Âàðèàíò 4: (a, b, c, f, g, h, j, k) = (1, 2, 3, 1, 0, 2, 0, −3) Âàðèàíò 2=Âàðèàíò 5: (a, b, c, f, g, h, j, k) = (−2, 6, 10, 2, 3, 4, 3, 2) Âàðèàíò 3=Âàðèàíò 6: (a, b, c, f, g, h, j, k) = (4, −3, 1, 2, 0, 10, 0, −8) Âàðèàíò 4=Âàðèàíò 8: (a, b, c, f, g, h, j, k) = (3, 2, 1, 2, −3, −5, −3, 2) 2. Âû÷èñëèòü íåñîáñòâåííûé èíòåãðàë ∞ −∞ δ0 aeibx +δ0 c sin(fx) gx3+hx2+jx+k dx, ãäå Âàðèàíò 1=Âàðèàíò 4: (a, b, c, f, g, h, j, k) = (0, 2, 1, 7, 1, 4, 4, 1) Âàðèàíò 2=Âàðèàíò 5: (a, b, c, f, g, h, j, k) = (1, 9, 0, 3, 0, 2, 3, 4) Âàðèàíò 3=Âàðèàíò 6: (a, b, c, f, g, h, j, k) = (0, −1, 1, 10, 2, 5, 5, 2) Âàðèàíò 4=Âàðèàíò 8: (a, b, c, f, g, h, j, k) = (1, −3, 0, −4, 0, 4, 2, 6) 3. Âû÷èñëèòü íåñîáñòâåííûé èíòåãðàë ∞ −∞ eax ebx+c dx, ãäå Âàðèàíò 1=Âàðèàíò 4: (a, b, c) = (1 + i, 2, 1) Âàðèàíò 2=Âàðèàíò 5: (a, b, c) = (3 − i, 4, 10) Âàðèàíò 3=Âàðèàíò 6: (a, b, c) = (−1 + 2i, −5, −1) Âàðèàíò 4=Âàðèàíò 8: (a, b, c) = (−1 − 3i, −3, −2) 4. Âû÷èñëèòü íåñîáñòâåííûé èíòåãðàë ∞ a 1 (bx2+cx+f)· √ x−a dx, ãäå Âàðèàíò 1=Âàðèàíò 4: (a, b, c, f) = (1, 1, 3, 6) Âàðèàíò 2=Âàðèàíò 5: (a, b, c, f) = (−1, 2, 4, 5) Âàðèàíò 3=Âàðèàíò 6: (a, b, c, f) = (0, 1, i, 5) Âàðèàíò 4=Âàðèàíò 8: (a, b, c, f) = (0, 2, −i, 3) 1