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

Q: Find the indicated midpoint rule approximation to the following integral. 2 sin 5x dx usingn=6…

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

A: Known integral formula:

Q: Use Simpson's 1/3 rule with (n₁ = 2), and Simpson -2 1 estimate tan-¹(2). [Hint: tan-¹ (2) = ₁²; dxl

A: Note: Since you have asked multiple questions, we will solve the first question for you. If you want…

Q: sin 20 arctan(sin 0) d0

A:

Q: Find the area bounded by the trigonometric curves y=sinx and y=cosx from; x== 3.459 square units…

A: Area bounded by the curve .

Q: Use Simpson's rule with interval h = 1 to determine the approximate value of 6 V(1 + x³)dx. Give…

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Q: Use an appropriate substitution and then a trigonometric substitution to evaluate the integral.…

A: By applying  trigonometric substitution

Q: The trigonometric integral fs sec² x (tan³ x - 2 tan7 x) dx is equal to

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Q: Use the Midpoint Rule with = 4 to approximate 0 tan x dx.

A:

Q: Evaluate the integral. arctan dx 1

A: For evaluating the given integral, we will use the concepts of integral by parts and integration…

Q: From the figure formed in integrating -dx, what is the term or value that is adjacent to the angle .…

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Q: After choosing the appropriate trigonometric substitution the integral -dx, becomes

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Q: Find the definite integral o tan(x)dx using strips of width for the trapezium rule correct to three…

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Q: The area between y= 2sinx and y = sin2x for 0<x ST is

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Q: Evaluate the following integrate 3 -dx 1+sinx

A: Multiply the expression in the given integral by (1-sinx)/(1-sinx) to evaluate the integral easily.

Q: Calculate the left rectangle approximation of 3x- dx using five subintervals.

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Q: Evaluate the indefinite integral. arctan dx

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Q: Use integration by parts to evaluate the integral sin(10x)/e^2x dx

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Q: What is the integral of 10pi(4-y)(sqrt(siny))dy from 0 to pi?

A: Let I=∫0π10π4-ysinydy Then, ∫0π10π4-ysiny…

Q: Use integration by parts to evaluate the integral. 3æ sin(z)dx

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Q: By using Beta function, the integral I tan(0) d0 is

A: To find value of integral∫0π2tanθ3dθ by using Beta function. Bm,n=ΓmΓnΓm+n…

Q: rea of the region between the sine curve

A: Here we have to find the area of the region bounded by the sine curve and the x-axis from π2 to 2π.…

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: Use the trapezium rule to find [2" dx taking ordinates with interval 0.25, in three decimal places.

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Q: Use the Table of Integrals on Reference Pages 6–10 toevaluate the integral. integral  tan 5  dx

A: Split tan5x into simpler powers tan3x and tan2x and change tan2x to sec2x-1 and simplify.…

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

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Q: 91. Prove the integration formula tanx dx = In | secx| + C (a) by using algebra and integration by…

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Q: Use the Errors in the Trapezoidal Rule and Simpson's Rule cos(4nx) dx

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Q: Find the indefinite integral. ∫arctan x dx

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Q: What is the value of integral /tanx dx ?

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Q: Use the Trapezoidal Rule with n = 7  to approximate integral 0 to 20  cos (pie x) dx. Compare your…

A: To Determine: Use the Trapezoidal Rule with n = 7  to approximate integral ∫020cosπxdx. Compare your…

Q: Approximate sinx dx using four trapezoids of equal width. On the interval (0, pi)

A: Trapezoidal rule

Q: Consider f(x) = sin(2x) + cos(4x), 0 ≤ x ≤ 1 Differentiate f at x = 0.5 using 5 point formula. Also…

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Q: Give an interval over which you could integrate to find the area of one leaf of the rose r = 2 sin…

A: r=2sin3θ

Q: Evaluate 0, dx by dividing the interval into 10 equal parts 8х-5 by using Simpson's one - third…

A:

Q: use a geometry formula to find the exact value of the definite integral.  5 dx on interval[-2,6]

A: Question is to find the exact value of the definite integral 5dx in the interval [-2 , 6 ]It is…

Q: Use Simpson's rule with n = 6 to approximate cos(a) dx Keep at least 2 decimal places accuracy in…

A: The solution is given below in the next step:

Q: The approximate value of dx by using Simpson's rule is 0.3480, then the error in the approximation…

A: Given Approximate value of the integral by Simpson's rule(Vs) = 0.3480 Now we will find the actual…

Q: Find the definite integral 5 tan(x)dx using strips of width for the trapezium rule correct to three…

A:

Q: The definite integral 'tan2(x) + sec2(x)]dx when evaluated is equal to AV3 + Br, where A, B are…

A:

Q: To approximate cos(x) dx would Simpson's Rule, Midpoint Rule, or Trapezoidal Rule give a better…

A: The exact value of the given integral is 1

Q: Use the trapezoidal rule with n = 4 to approximate cos(x) de Keep at least 2 decimal places accuracy…

A: Given that: ∫14cosxxdx and n=4

Q: f sin-¹(x) dx

A:

Q: Use integration by parts to evaluate the integral. sin(In(5x))dx

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Q: Use the Composite Trapezoidal rule with h = approximate the improper integral 1 sin 2x dx to

A: Given,        ∫01sin2xx3dx=

Q: Find the trigonometric integral ∫sec4(x/2 ) dx

A: To evaluate the trigonometric integral , ∫sec4x2dx Solution: Put x2=t in the given integral we get,…

Q: Integrate this item using (parabolic) Simpson's rule, with interval width of 2.00 units. x tan x +…

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Q: Use differentials to approximate tan (43°). Round to 4 decimals.

A: Approximate to tan(43°) using the differentials ,

Q: Find when 4= SINX Thuen dy (sinx) (ar f(s wheve for 0<x< M2 tanx taux a=?

A:

Q: The approximate value of| dx by using Simpson's rule is 0.3639, then the error in the approximation…

A: Approximate value of ∫161x4dx by using Simpson's rule is 0.3639 To find the error in the…

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.