Use 4-segment the trapezoidal rule to numerically integrate f(x) = f(x)=∛(44x-4) from a = 44 to b =4 Find the difference between the approximate answer and the exact answer.

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Q: evaluate using Integration by Parts.

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Q: Find the solution of the integration using trapezoids and Simpson's 1/3 rule and compare the…

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Q: sec( c)+y dy e sec do

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Q: By Simpson's method, find an approximation for [(x³−2x³)dx_(n=4) 0

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Q: Suppose that 2 J of work is needed to stretch a spring fromits natural length of 30 cm to a length…

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Q: The maximum value of y = sin x, 0 <= x <= 2p, isand occurs at x =__________ .

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Q: solve the differenhal equa hon by varianon of parameters y" + 3y't 2y 7 te* y (x)

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Q: What is the value of the integral ∫2−2 max [1,x2] dx ?

A: This question is related to integration.

Q: a) Estimate the length of this arc with the length of the line segment joining the endpoints of the…

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Q: Verify the power rule for integration fx'dx= n+1

A: Given a power rule of integration,

Q: (b) Use Integration by parts to show that ·4 In x ~dx= =-+2ln.x) +C

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Q: • Use the trapezoidal rule with n = 14 to estimate: -dx √√1+x²

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Q: Use the 4_segment trapezoidal Rule to numerically integrate. S(0.2 + 25x + 3x²) dx

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Q: (b)/ Use the Trapezoidal Rule with n = 4 to estimate (x' + 1)dx.

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Q: Find the smallest positive root by using fixed- point method f (x) = In(3x)– x² +2 %3D with three…

A: Given: fx=ln3x-x2+2. We have to find the smallest positive root by using fixed-point method with…

Q: Use Trapezoidal Rule with (n- 4) to find the integral dx x-1

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Q: Use the composite trapezoidal rule with the step length h = 0.1 to evaluate sin x -dx, in six…

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Q: 22. Use the Trapezoidal Rule with n = 4 to approximate 1 (x− 1)² dx

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Q: What is the isogonal trajectories family of curves x² - y² = a which intersects at an angle of ∅ =…

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Q: When two particles start at the origin with velocities v(t)=cost and u(t)=sin2t, how many times in…

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Q: A stone, projected vertically upward with initial velocity 112ft/sec, moves according to s = 112t −…

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Q: The integrating factor of Y + 3y cscx= cotx is?

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Q: Q2// Use Euler's method (with all details) to find approximate value of y when x = 3 of = 2y-2x²-3,…

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Q: What is the value of the function xcosnxdx if we integrate it using Kronecker' smethod?

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Q: use taylors formula to find the cubic approximation to f(x,y)=sin(6x+y) near the origin

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Q: Use the Midpoint Rule withn= 3 to approximate the integral %3D 13 (- 9z - 3a")daz 9x 3x) dx

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Q: In integrating the function fx cos(3x) dx using integration by parts, what would be your v?

A: Solution

Q: 1 a) x²e-x dx

A: Use the formula of integration by part and finally put the limit  to got the answer

Q: In integrating the function fx In 5x dx using integration by parts, what would be your v?

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Q: Use the Trapezoidal Rule with n = 4 to estimate f, (x³ + 1)dx.

A: We have to estimate ∫-11x3+1dx by using the Trapezoidal rule with n = 4.

Q: Find the root of the cubic equation 4x3 + 3x2 – 8x – 2 = 0 in the domain [ 1 , 2 ] using numerical…

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Q: Use the method of Variation of Parameters to solve. SHOW WORK. у" - у' — 2у %3D 2е-t

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Q: The approximation of I = f(x-3)** dx by composite Trapezoidal rule with n=4 is:

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Q: If integration using u-substitution technique is used to solve for ∫2e2x1−e4x dx/square root of…

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Q: Use the composite trapezoidal rule with the step length h = 0.1 to evaluate sin x = 5.² in six…

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Q: What is the value of the integral ∫2−2 max[1,x2]dx ?

A: Value of the given integral is 2x [1- ((x^2) /3) ]

Q: 2. Use the Midpoint Rule with n = 4 to estimate (x² + 1) dx %3D

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Q: Find a root of a equation f(x) = 2x³ - 2x - 5 Using secant bisection method when the initial…

A: Given : 2x3-2x-5=0Let  f(x)=2x3-2x-5

Q: Q2 \ Evaluate .1 dx by using trapezoidal rule. 1+x2

A: See the details solution in below

Q: The minimum value of n required to approximate xe dx by composite Trapezoidal rule with an error…

A: Find the minimum value of n required to approximate ∫02xe-xdx by composite Trapezoidal rule with and…

Q: sin x dx B) - 7 1+ 2 1+ A) -(1+ 2) 7 C) - 2 1+ D) 4 8

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Q: Use Variation of Parameters to solve the DE y" – 4y %3D

A: Given differential equation y''−4y=e2xx Write the auxiliary equation m2−4=0 ⇒m2=4⇒m=±2 Hence,…

Q: Find atleast three approximations of a solution of the equation f(x) = x – 2x = 0 by Newton Rampson…

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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.