The trapez rule is an approximation method to find approximate value (T,, neN) of an definite integral [f(x)dx as follows: 1) h T, Here, a = x, x = X, +k - h, k =1,2,...,n, b-a h =- Use Trapez rule to find approximate value of In(2) = | 2x -dx and fill the blanks in 1+x? the Table below. (Note: Use a calculator and get 6 significiant digits after decimal point.) Absolute Relative Absolute True Approximate Approximate Error T, Error Error E, = In(2)– T|| x100% 4 6 8 2. 00

Q: Use Midpoint Rule, Trapezoidal Rule and Simpson's 1/3rd and 3/8th Rule to approximate the integral.…

A: To approximate the value of the given integral using midpoint rule:

Q: Find the exact value of the integral. (No decimal approximations accepted) 1/2 x cos(x³) dx

A: Given problem is :

Q: Show that 2x° dx = [; 2r° dx + f zr* dx + [,2x° dx %3D

A: Given that,    ∫142x2dx=∫122x2dx+∫232x2dx+∫342x2dx

Q: Use the Fundamental Theorem of Line Integrals to calculate exactly. F-6 sin(ox +)+ sin(6x )j along…

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Q: Find the area A of the region that is bounded between the curve f(x) = -2 sin () and the curve g(x)…

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Q: Show that ∫0∞ e-x 2 dx = ∫10√(-ln y)  dy  by interpreting theintegrals as areas.

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Q: Determine h and N to approximate the integral e-t" dt within an accuracy of G 10-5 using the %3D (i)…

A: ∫01e-t2 dt a) Composite Trapezoidal Rule Error=h2b-a12|''Cn ⇒EnTt≤10-5 calculating the derivative;…

Q: For the area bounded by the x-axis and the function f() = x² – 3x + 2, using Euler's Forward…

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Q: Consider the graph of the integrand f(x) = 3x on the interval [0, 1]. What well know formula can you…

A: The value of definite integral gives the signed area. This concept is explained in the step 2.

Q: Q3. Use tabular integration by parts to evaluate the following Integral (x² +x+ 1) sin x dx

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Q: Find the indefinite integral using integration by parts with the given choices of u and dv. (Use C…

A: We will use integration by parts to solve this.

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

A: We need to find the approximate values of ∫π4π2ln(tan(x))dx using trapezoidal and Simpson rule given…

Q: What is 'a' called in S, f(x)dx? a. Lower limit b. Integration C. Upper limit d. Limit of the…

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Q: x sin (x²) cos(x²), from a = 0 to b = 3. Estimate the integral of the given function, using %3D…

A: The given function is fx=xsin3x2cosx2. Here, a=0, b=π2, and n=8. We have to approximate the integral…

Q: 4. Evaluate the integral using Trapezoidal and Simpson's rule with h = 0.5, 0.25 and 0.125. = 1+ 2x3…

A: Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

Q: Since the integral y(x) = Sof(t) dt with variable upper limit satisfies (for continuous f) the…

A: Given - Since the integral yx = ∫0xftdt with variable upper limit satisfies (for continuous f) the…

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

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Q: Find the inde finite integral. (Use C for the constant of integration.) -5 dx (x2 + + 5)3/2

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Q: Find the critical point of the function f(x, y) = – (25x + 5y + In(|x + y[)). c = Use the Second…

A: (a) Given that, f(x,y)=-(25x+5y2+ln(x+y)) This can be written as, f(x,y)-ln(x+y)-25x-5y2 Now take…

Q: Use the methods of (1) left Riemann sum, (2) right Riemann sum, (3) trapezoidal rule, (4) parabolic…

A: According to our company's guidelines I can only answer first three subparts of the question since…

Q: Use Cauchy's Integral Formula and Cauchy's Integral Formula for Derivatives, when appropriate, to…

A: The given integral is: ∮Cz2+5z2-6iz-5dz, where C is the circle z-6i=1.3 Cauchy Integral formula: Let…

Q: show that the differential forms in the integralsare exact. Then evaluate the integrals

A: Show that the differential forms in the integrals are exact. Then evaluate the integrals.…

Q: (1,2) (b) Set up a definite integral that is equal to the arc length of the portion of the circle…

A: Note:- As per your request i am solving here question no. 3 part B only.

Q: Use geometry to calculate (without integrating): o V16 – x2 dx Note that f (x) = v16 – x² is the top…

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Q: Find the length of the function of r over the given interval. If you cannot evaluate the integral…

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Q: hat are the new limits of integration after applying the substitution u = 6x + x to the integral /…

A: Given query is to find the limit after applying the substitution.

Q: Find the approximation of the integral. 1= [e*dx Using Romberg's rule derived from Trapezoidal rule…

A: Given integral I=∫01e-x2dx Here we use Romberg's rule derived from Trapezoidal rule for 1,2,4,8…

Q: Calculate the approximate to the integral -5 (24 +2x² − 3)dx, by the composite midpoint rule with…

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Q: Find the approximate integral of 4 1 * -dx In x 2 when n=10 using a) the Trapezoidal Rule, b) the…

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Q: Using the trapezoidal rule with n = 4, estimate the integral / (x (x+1)² dx.

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Q: find the derivative y= the integral from 0 to the square root of x 5tcos(t^4) dt show all work

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Q: Let L be the length of the curve y = ln x from (1, 0) to (e,1). (a) Integrating with respect to x,…

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Q: (b) 3 – cos(x) 2

A: Follow the procedure given below.

Q: 4 | a sin(3y+ x²)dydx, 2 a) Sketch the domain of integration on an (x,y)-plane. b) Set up the…

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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: What is the formula for the total distance traveled by an object with a velocity v(t) = O - ¹ sin…

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Q: Use Simpson's rule (n = 4-this means that there are 2 rectangles for the trapezoid rule and 2…

A: To evaluate ∫-11x2-1 dx with n=4 using Simpsons Rule

Q: Let u = 1– 16x². For the integral with respect to u, one limit of integration will be 1. What is the…

A: To find:- For given integral need to find new limits when we substitute u = 1-16x2

Q: 3. Change the order of integration sin dydx. Hence, evaluate the integral. y

A: Sol ∫0π∫xπsinyydydxChange order of integration =∫0π∫0ysinyydxdy

Q: 0.5 cos x In(3 sin x)dx = COS I %3D 0.1

A: Definition used -   U substitution - When there is a composite function multiplied by the…

Q: if Zcand Zp is complementary function Particular integral for the equation f(x X F(x,y) respectively…

A: This is Partial differential equation.

Q: ROBLEM 1: Evaluate the integral ,(1 – x – 4x° + 2x*) dx a) Analytically b) Single application of…

A: “Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

Q: 2. Estimate the integral using Simpson's approximation rule with n=4: sin t dt

A: To estimate:∫0πsint dtn=4

Q: In The value of the definite integral flm 12 √ex - 9 dx is in the form F(b) - F(a), where a JIn 9…

A: To evaluate: ∫ln⁡9ln⁡12 ex−9dx Let I =∫ln⁡9ln⁡12 ex−9dx Given: ∫ln⁡9ln⁡12 ex−9dx = c3-dπ Let ex−9=…

Q: Show that the differential form in the integral is exact. Then evaluate the integral. (1,2,3)…

A: Given : ∫( 0 , 0 ,0)( 1, 2, 3)  3 x2y dx + ( x3 - z3 ) dy - 3y z2 dz

Q: 2. Using the Simpson’s rule with N = 4, find as accurately as possible numerical value of following…

A: Given that the integral is ∫1∞e-x22dx and n=4. Now find  h=b-a2=∞-12=∞h=∞ The value of h is…

Q: Use the Trapezoidal rule to approximate the integral from upper limit 1.05 to lower limit 1 e^-2x^2…

A: To find- Use the Trapezoidal rule to approximate the integral ∫11.05e-2x2 dx. Find an upper bound…