2. By finding an antiderivative, evaluate each of these integrals, where the path is any contour between the indicated limits of integration: a) St¹² & ez dz; Cr+2i b) [™+ ² cos ( - ) dz: Ans. (a) (1+i)/л; (b) e+ (1/e); (c) 0. (c) fª (z − 2)³ dz

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Q: After the appropriate substitution, which of the following yields an arcsine function upon…

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Q: a) By using integration by parts, find the integral Inx dx. b) Hence, find In Vx dx.

A: We have to apply the integration by parts.

Q: 14. Evaluate the integral: (x² + 3x)° dx A. (x* + 30)' + C 3 x* + 3x' + C C. +C (x² + 3x) + C В. D.

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Q: (LT3.a) Use the Fundamental Theorem of Calculus to find the exact value of the definite integral √2…

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Q: 2. Evaluate the definte integral S 2 ln 3 xe -x²/2 dx.

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Q: P4. Find the following integral using integration by parts: sin ¹(4x) dx cos(In x) dx (3x + 5)…

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Q: Evaluate the following integration: 3x-2)dx Using trapezoidal rule for 100 and 1000 equal segments.

A: Given integration is ∫02x5+3x3-2dx Solution a: let f(x)=x5+3x3-2 Using Trapezoidal rule Here equal…

Q: Use the graph of f(x) below to evaluate the given integrals: a. xp (x)f*J q c. f) dx d. f) dx Lf) dx…

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Q: Q6. A: Evaluate the integrals: sec x dx dx 2) L, | VIn(secx+ tan x) -2 (4+x²)3/2

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Q: 2. Evaluate the following integrals using integration by parts: (a) fa? sin?r dr, (b) Se cosz dr.

A: integration of uv  u int (v) dv - [int ({ du/dx } int (v)) dv]

Q: by reversing the order of integration: In y cos(ex-1) dx dy

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Q: 1. Use contour integration to evaluate the following integrals dx (1+x²)³ · Sº i. x dx 11. 5. (x² +…

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