-0∞ x-sin(x) Compute the integral t dx by the Residue Theorem. You must x4+4 show all calculations.

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Q: 8.8.16. Use a known Taylor polynomial with n nonzero terms to estimate the value of the integral.

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Q: Q1 (a) Integrate the following definite integrals using suitable method: (i) S, tan-1 x dx (ii) a dx…

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A: Given integral is ∫x(1-x2)5dx Let, 1-x2=t⇒-2xdx=dt

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Q: Fra) = Sin (2t) Find the 7h taylor Polynomial of

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Q: Evaluate the integral. x² - 81 | V=² x x² - 81 | Vx² x √x². 81 X √x². 81 X x² - 81 X 1² 1² - dx = -…

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Q: 9-10 Use the Midpoint Rule with n = 4 to approximate the integral. 9. 2² dx

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Q: Question 1 Evaluate the following integrals using residue theorem: Lx (2² + 9) (2² + (b) 2³ sin uz…

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Q: Solve the integral. 3. Find the second-degree polynomial P(x) such that and P(0) = 1, P'(0) =…

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Q: 5x dx. - 6 Compute the integral x2

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Q: 17. The third-order Taylor polynomial P,(x) for sin x about is 4 (A) (*---") (x) 3! | (B) J2 1+(x (x…

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Q: 9-x2 B: Find the integral S 18-x2-y xydzdydx.

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Q: 2. Use the Definition of Residue to show that: dz -ni 3 Izl=1z sinh z Where 0 < |z| < T.

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Q: Use the second Taylor polynomial of f(x) = ln x at x = 1 toestimate ln 0.8.

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Q: Section 11.6: Calculus of Vector-Valued Functions - #49

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Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.