The actual error of the approximation of I = x² sin (x³) dx using composite Simpson's rule with n=4 is:

Q: Find the integral. er sin(5x)dx - IT

A: Known integral formula:

Q: evaluate using the appropriate method or combination of methods.

A: Use 2sinA*cosB=sin(A+B)+sin(A-B) formula

Q: Given: y = x - sin(2x) Find: dy dx 0 - cos²x 2 ○ - sin² x 01+ cos²x O sin²2 X

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Q: Use integration by parts to show that for n > 2: / sin" x dx: 1 sin- x cos x + /sin-2 x dx.

A: To evaluate: ∫sinnx dx

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

A: What is Simpson's Rule: Simpson's rule is a tool to approximate an integral. It is the process to…

Q: Use integration by parts to show that, for n > 2, 1 cos a sin"-1 n 1 sin"-2 xdx. n - sin" xdx = x +…

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Q: S sin x In(cosx) dx

A: To evaluate the integral: I=∫sin x(ln (cos x)) dx Substitute  cos x=t⇒-sin x dx=dt⇒sin x dx=-dt

Q: Use Simpson's rule with n = 4 to approximate cos(x) dx 1

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Q: The approximation of I tanx dx using composite Simpson's rule with n=5 is: = None of the choices

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Q: Evaluate the definite integral. sin x dx -dx J12 I+cos² x

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Q: The approximation of xln(x + 3) dx using two points Gaussian quadrature formula is:

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Q: Find the theoretical error bound in approximating SN" sin(x?) dx using Boole's Rule.

A: The theoretical error bound in approximating the integral∫0πsinx2dx using Boole's rule is shown…

Q: Evaluate the integral.  integral sin 3  x cos 5x dx

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Q: Only one of these calculations is correct to evaluate the definite integral V sinx dx Using the…

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Q: Evaluate the definite integral. 1. S(sin(2x) – cos(2x)) dx

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Q: .Find a reduction formula for ea* sin" x dx. Hence evaluate e* sin x dx. 3

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Q: Evaluate the integral. sin(5.x) sin(4x) dx

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Q: Find a root of an equation f(x) = cos(x) - − using Newton Raphson method

A: Let us start solving the problem step by step  Given  Cos(x)-(x/6)=0 Let f(x)= cos(x)-(x/6) We will…

Q: Evaluate 1 ei sin x cosx dx using Simpson rule with h = 20

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Q: Use a suitable substitution to find the indefinite integral S csc(sin 0) · cos(0)d0

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Q: Find the integral of sin(8x)sin(x)dx

A: on doing integration

Q: 2. Find a root of f(x) = 6 Sin (x)e* + 1 using Newton Raphson Method accurate to 5 decimal places.

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Q: 3 Estimate the error if S10 (Simpson's rule with n = 10) was used to calculate sin(4 x) dx .

A: I=∫03sin4xdx Integrating it- I=-cos4x403=-cos124+cos04=1-cos124=0.0054

Q: What is the definite integral of sin^5 (x) cos^3 (x) dx if the lower limit is zero & the upper limit…

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Q: 2. Using both trapezoidal and Simpson rule, find the approximate values for the integral SIn(tan x)…

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Q: What is the integral of sin^5 x cos^3 x dx if the lower limit is zero and the upper limit is T/2?

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Q: Lnx sin 2x dx

A: Use the properties of definite integral and solve the question.

Q: From 0-2 sin(x^2) dx using trapezoidal rule with n=4 as well as midpoint rule with n=4

A: Trapezoidal rule=∫02sin2(x)......(1)As we know that accoding to trapezoidal rule…

Q: S sin(4x +3)cos(3x – 5)dx -

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Q: Use Property 8 to estimate the value of the integral.

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Q: Evaluate the integral.  integral sin 6  x cos 5x dx

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Q: The approximation of I tanx dx using composite Simpson's rule with n=5 is:

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Q: Find the indicated midpoint rule approximation to the following integral. .3 2 sin 7x 2 x dx using n…

A: Calculate the delta x and the f(xi) for the given integral.

Q: The most general antiderivative of x sin(3x) is

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Q: Find the trigonometric integral ∫sin x cos4 x dx

A: Consider the integrals: ∫sinx·cos4xdx…

Q: Use integration by parts to verify the reduction formula.

A: We have to verify the reduction formula using integration by parts: ∫sinn x dx=-sinn-1 x cos…

Q: 3. Use Simpson's rule to calculate x² sin x dx to within 2 × 10-5 of the exact value.

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Q: The length of one arch of the curve y = sin x is given by L = | VI + cos² x dx. 0, Estimate L by…

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Q: f sin-¹(x) dx

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Q: Evaluate the integral.  integral sin 3  x cos 2 x dx

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Q: Use integration by parts to evaluate the integral: sin(-10r) dr e12r

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Q: Find the definite integral of sin x -dx 0 1+cos x

A: Given: I=∫0π2sin x1+cos xdx

Q: Find the trigonometric integral ∫sin2(x/2)  dx

A: From the given data:

Q: Find the general indefinite integral.

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

A: Given: y'=2y-2x2-3 , y(0)=2 , h=0.3. We find y(3) by using Euler's method. The formula for Euler's…

Q: The approximation of 1 = f*cos(x³ - dx using composite Simpson's rule with n= 3 is:

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Q: Evaluate the integral. 2 sin -1 x dx

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Q: Compare the Trapezoidal rule and Simpson's rule approximations to x sin x dx and find a bound for…

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Q: (sin-l x)² dx V1-x²

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Q: Consider 3x+ sin x − ex= 0, using Secant Method with initial points X0 = 0 and X1 = 1, calculate the…

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