3. Evaluate the following integrals, using the residue theorem. (a) f. sin z dz (e) £ 1 dz (c) dz Iz|=1 28 |z-1|=1 |2|=2 COS z (b) . ez dz 1 (4) f. zp Izl=1 sin z (f) £ tan z dz Izl=2 Iz-1/2|=3/2 Only question b and c plz

Q: 3. Compute 82 f + 0x2 8 f òy2 for the function f (x, y) = ea sin (ay).

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Q: S²10 f(x) dx = -10, Use these values to evaluate the given definite integrals. 2 1) ²³ (f(x) + g(x))…

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Q: 1 dx 49 1 42 49 arcsin 7x) - 49 sin 2 arcsin 7x+C (2x) 2 (1 x)) X

A: Given, ∫ x249-x2dx

Q: +0 So 250 3 2f(x) dx = 4. (a) Using properties of definite integrals, find so f(x) dx. (b) Using…

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Q: 2. Use the Fundamental Theorem of Calculus to find: (a) (b) (c) cx³ de fort+3* cos²¹(y) dy. dx d dx…

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Q: cos(x) dx = dx. Use - 0o (1+x²)² o cos(x) 00 cos (x) Compute Jo 1+x²)² dx. Note that 2 (1+x2)2 the…

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Q: Using the substitution t = tan(), the integral 2 dx sin(x) – 78 cos(x) can be written as dt 39 – t-…

A: To make substitution and re write the given Integral.

Q: 2. Evaluate the integrals. Va² + 16 (a) (HARD) dx. x2 (b) / u4 sin(u") du.

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Q: 5. Find L{f(t)} a. f(t) = sin?(t) + t b. f(t) = n² – 8e¬2t + (et + 1)² | c. f(t) = F, sin yt -cos…

A: As per our limit we can solve only first three subdivisions if you want the answer for other…

Q: We would like to evaluate d sin(t?)2tdt dx Compute f (x) = S*, sin(t²)2tdt Find f' (x). (a) (b) (c)…

A: To solve the problem uaing fundamental theorem of calculus

Q: .. a) Show that sinh(2x) sinh(x). = 2 sinh(x) cosh(x), using the exponential definitions for cosh(x)…

A: Hyperbolic functions are defined using exponential functions. The hyperbolic function sinhx is…

Q: 2² sin(1/2) z 7 0, f(2) = z = 0.

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Numerical Integration

In a mathematical investigation, numerical integration comprises a wide group of calculations for computing the mathematical estimation of definite integral, and likewise, the term is moreover in some cases used to depict the numerical solution of differential equations. The most important aspect of this theory is error analysis.