4. Using the Cauchy Integral Formula for Derivatives, evaluate the following integral 2 +1 dz 2 + 2iz3

Q: Prove that 1 + p'2 p4 where primes denote differentiation with respect to 's'. 1. x"2 + y"2 + z"2 %D

A:

Q: 5. Evaluate the definite integral (1+Inx) а. b. S dx. 2x+3

A: a) ∫1e1+ln x2xdxb) ∫-1112x+3dx

Q: 3. 'Evaluate the integral. 5 dx х0.2

A:

Q: 8 cos" 2πt dt

A:

Q: (4) 3. Use implicit differentiation to find dy/dx of the following: x² - 5xy + y³ = 21

A: As per policy only first question is answered. Please refer to the image below

Q: 2.Find the following indefinite integral without substitution. S sec y (tan y- sec y)dy

A:

Q: Evaluate the definite integral. 3 3 dy y /1

A: As per bartleby answering guidelines we are allowed to answer only one question per post. Hence…

Q: 13. Evaluate the indefinite integral fx cos x dx x sin 2x cos 2x a. + c 2 x sin 2x cos 4x b. + c 2 2…

A:

Q: 19. Evaluate the integral Z √(x^2 − 9) / x^3 dx

A: firstly divide the numerator by denominator part by part to simplify the integration

Q: 6) Use the successive approximations method to solve the following Volterra integral equation: u (x…

A: The Volterra integral equation is given as u(x)=x22-∫0x(x-t)u(t) dt. We have to solve the equation…

Q: Use Part 1 of the Fundamental Theorem of Calculus (and properties of definite integrals and the…

A: Solve the following

Q: Evaluate the definite integral. 3 2esin ( z ) cos(x)dx 3

A: Given that: ∫0π32esinx.cosxdx

Q: Use the bise ction to approximate the solution of F(X)=Vx - cos X = 0 accurate to within 10 -3 on…

A: Bisection method: In order to find root of equation f(x)=0 in a,b such that f(a)f(b)<0 Bisect the…

Q: (4)Evaluate the definite integral (a)S(1 + sin x )£x 1/2 (b) [ (2t + cost)dt -*/2 x +1

A: As per the Guidelines, I will answer the first 3 Integrals. For the fourth one please repost the…

Q: - Using the integral definition of gamma function show that T(7) = 61(6)

A: Integral definition of gamma function is Tx=∫0∞tx-1e-tdt . Put x=7 in Tx=∫0∞tx-1e-tdx and simplify…

Q: 2x(x+, こメP

A: Solve

Q: 4. Find the Cauchy principal values of the following integral: dx. (x²+1)(x²+2x+2)

A:

Q: 1 Evaluate the improper intergal | dx (x2 + 9)° using the residue theorem.

A:

Q: 12.)Express lim E(3(x;,)² – 5x, + 2)Ax as a definite integral on the interval [0,1]. i=1

A: The given expression is: limn→∞ ∑i=1n 3xi2-5xi+2∆x    on interval [0, 1]   The definite integral  on…

Q: 2. Find the indefinite integral: S (Vã+ - x + - 1) dx 6 .3 X X

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Q: Obtain a formula that expresses the integral [cos". cos" x dx

A:

Q: please explain how to do question 7c

A: The given integral is ∫(1-3x)4dx.

Q: In 2 10e a 4.

A:

Q: 5. Find the indefinite integral. A) f dx (x-3)Vx -6x+5

A:

Q: 11 By reversing evaluate the -3 -9 ffix the orders of integration following integral x cos(y) dy dx

A: Given integral ∫03∫x29 xcosy2dydx The region bounded by  y=x2 , y=9 , x=3 and x=0

Q: In(x) Differentiate the function F(x) = | cos(e e') dt (for x>0)- 1/x Show and justify your work.…

A: The given function is: Fx=∫1xlnxcosetdt To differentiate the given function.

Q: Use integration by parts to establish the reduction formula: Jx" cos x dx = x" sin x – n x*-1sin x…

A:

Q: 4. Use residues to evaluate the improper integral 1t r4 a + x2 dx; where a is a real constant.

A:

Q: O f(3x² + sec² 2x) dx

A: Given query is to find integral.

Q: Q1)Evaluate the following integral: 2 1-x dx 1+x2,

A: 1 We have to evaluate the integral ∫021−x1+x22dx. Now,…

Q: 7. Use integration by parts to prove that for any positive integer n, п - 1 Scos | cos"x dx = 1…

A:

Q: 7. Find the indefinite integral. (a) + sec , | dx = 4 In |x| + tan(x) +C (b) / )Lanr dx = In |In x|…

A: Given that: (a)∫4x+sec2xdx(b)∫1xlnxdx(c)∫x4-3x2+5x4dx

Q: 6) Use the successive approximations method to solve the following Volterra integral equation: 2 и…

A:

Q: (4) 3. Use implicit differentiation to find dy/dx of the following: x2 – 6xy + y3 = 24

A:

Q: 3. fx² √9-x² dx

A:

Q: 7. Evaluate the definite integrals: a) L, (x2 +1) dx b) 3x dx

A:

Q: Show detailed solution for the following integral: (Non-anonymous questionO) S tan'z sec³z dz 7

A:

Q: dx 2.) S 4+ x2

A:

Q: 1. Evaluate the indefinite integral. Hint: U-substitution. 3 dx x In x

A: ∫ 3x lnx dx 3∫ 1lnx·1x dx

Q: 3. Find the derivatives of the following in two ways: -by evaluating the integral and…

A: Here we solve this Question by  First integral and find derivative  By first fundamental theorem of…

Q: Evaluate the integral: sinh 3x csch 3x dx coth 3x "+C 3 coth X +C 3 - coth x +C - 3 - coth 3x +C 3

A:

Q: evaluate the Cauchy principal value of the given improper integral. roo 1 dx 6x + 25 | roo x2 dx (x2…

A: The Cauchy principal values of the given improper integrals areevaluated as shown below.

Q: S 5(x2 + 3)²dx

A: To evaluate the integral: ∫015x2+32dx. Solution: Power rule of integration states that:…

Q: Find the derivative of y with respect to x. y = tan(In 4x) O A. x/1+ ( In 4x)2 1 О в. 1+ ( In 4x)2 4…

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Q: The following differential is separable: dr = b(cosxdr + rsinxdx) true or false?

A:

Q: Find a formula involving integrals for a particular solution of D.E y" + 3y" – y' – 3 y = tan x

A: In this question, we find the particular solution of the differential equation. Here, we used the…

Q: 1.Evaluate the following integrals and check using differentiation: d 5-5t dt 10 +2.12e- . (a) 0.5t…

A:

Q: 2. fx²5-x' dx

A: ∫01x25-x3dxapply u substitution;take, u = -x3;du = -3x2-du3=x2then our equation can be written as…

Q: 1. Integrate by parts and evaluate x cOS x dx 0, а. b. In(x²) dx 1 In x dx x5 С.

A: By using Integration by part  ∫udv=uv−∫vdu

Q: 11. Evaluate the definite integral S" dx. x+a?

A: Topic:- definite integration

Confidence Intervals

When we calculate intervals in probability and statistics, it can be simply termed as finding out a confidence interval. The confidence interval is usually calculated from the data set which is observed. The value of the parameter that needs to be calculated is present here only.