What is the value of 'h’ in evaluating [ (3x² + 3x – 5)dx, using Simpson's rule, taking 10 subintervals ? a. 0.1 O b. 1 c. 0.2 O d. 0.5

Q: Evaluate J by means of Simpson's rule with n = 2m =20 and h =0.05 J= exp(-x²) dx Answer in 4 decimal…

A: f(x)=exp(-x2)h=b-an=1-020=0.05 table for x and y value: x 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4…

Q: What is the formula that would be used to calculate the trapezoid approximation of ST 2s in x dx…

A:

Q: Find n so that 27 en+1 – 1 < 0.05? 2 (n + 1)(n + 1)! Use the information above to calculate eet dx…

A: For (b), We need to find n so that 272en+1-1n+1 (n+1)!&lt;0.05. Notice that solving this…

Q: Use Simpson's Rule to evaluate the following. n = 10 +3 1 dx J-3 1+x²

A: SOLUTION-

Q: Evaluate the following integral. x - 15 dx x³ - 2x? +x * - 15 dx = - 2x² +x

A:

Q: Q4 Evaluate the fo ng In10 1- 4sinh? () dx 4 2 cosh(tane)sec20d0 - 4. 0rions in term of

A: (1) To evaluate: ∫0ln 104sinh2x2dx Let I= ∫0ln 104sinh2x2dx We know that 2sinh2x = cosh2x-1

Q: What is the value of rez+1 ? 1+e-z df (0), where f(r) = dz Give your answer as an integer or as a…

A:

Q: make the given substitutions to evaluate the indefiniteintegrals. ∫4x3/(x4 + 1)2 dx, u = x4 + 1

A: Now put

Q: 1. Approximate dx using each of the following.

A:

Q: How large should n be to guarantee that the Simpson's Rule approximation to 19ex2 is accurate to…

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Q: e" cos x dx

A:

Q: The integral 2n / 14xe dx can be done with the substitution u - and du= dx.

A: Step 3Given,2π∫14xe-x2dx

Q: Use Simpson's Rule to approximate the value of the definite integral 2x dx with n = 8. a. 16.9283 b.…

A: Simpson rule formula is: ∫082x4 dx≈∆x3f(x0+4f(x1)+2f(x2)+4f(x3)+...+f(xn))...(1) Here, ∆x=8-08=1,…

Q: 1. Which of the following values would be obtained using 10 circumscribed rectangles of equal width…

A: The integral is  ∫01 x2 dx

Q: The integral S₁ substitution is used? dx (x²+4)² can be transformed to which of the following when…

A: Let's integrate by using trigonometric substitution.

Q: Given that L 1125 · x² · In(*) dx = 1+ 2e³ 8 select which of the following values are correct for L.…

A: Given integration is                                    ∫25L1125x2ln5x28dx=1+2e3 we have to find L…

Q: The approximation of tanx dx usmg composite Simpson's rule with n-S is. O None of the choices O 0…

A: Given that I=∫01tanx dx and n=5 by using simpsons rule Simpsons rule…

Q: make the given substitutions to evaluate the indefiniteintegrals. ∫2x(x2 + 5)-4 dx, u = x2 + 5

A: Consider the given integral: ∫2xx2+5-4dx=∫2xx2+5dx-∫4dx Substitute u=x2+5→du=2xdx in the above…

Q: Use the Trapezoidal Rule to approximate the value of the definite integral x*dx with n = 4. a.…

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Q: 25) Find the Valne oF e dx, by Simpson's ra rule, 3. uSing 6 subintervals, correot to Four decimal…

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Q: Evaluate the following integral:  cube root of 1-3x dx

A: We will evaluate the integral as following.

Q: I Evaluate the following expressions by basic integration: dx 2. ,(x + 3)(x – 4)dx

A: Given

Q: Find the x-and y-intercepts of the rational function   See picture

A: The given rational function is,

Q: Q4. Consider the following integral. e3xsin(2x) dx where x is in radians The true value of the…

A:

Q: evaluate the following intergertal     (e−x + 2x)2 dx

A: Given integral is By using the identity (a+b)^2=a^2+b^2+2ab, we get

Q: On what interval is the formula d/dx(tanh'x) = 1/(x² – 1) valid?

A: ddxtanh-1x=1x2-1

Q: Determine how large the number a has to be so that 1 dx

A: We have to find out the value of a .

Q: Refer to the image attached

A:

Q: 2. Evaluate the following definite inte i) dx -4 1 5 x+3 )鳥) 6e-2x dx A3-e-2x

A: We have to find

Q: Evaluate and simplify the following integral: e* + e²x -dx 1+e2x

A: Solution: The objective is to find the value of the given integral

Q: 1 dx x(In x)*

A:

Q: Evaluate Vcosx + sinx dx by using trapezoidal rule , taking n = 4, correct to four decimal places…

A:

Q: 1. Using n = 4 equal-width rectangles, approximate [(x²+8) dx . Use the left end-point of each…

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Q: (c) For what values of a <ß is the integral √ √e-at - e-ßt dt To

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Q: Evaluate the following integral "/2 (8 + 4cosx)dx a. Single application of the trapezoidal rule b.…

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Q: Evaluate the following integral (1 – e *)dx using a composite (Number of segments, n= 6) application…

A: Use Simpsons 3/8 rule:…

Q: Evaluate V16-x² dx dx be? Explain Then, what would the value of the integral 1+V16-x 0.

A:

Q: Using trigonometric substitution, the integral -dx would result to M 9-x2 N?dt,what is M and N? (N…

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Q: Evaluate J by means of Simpson's rule with n = 2m=10 and h = 0.10 = [*exp(-x²) dx Answer in 4…

A: f(x)=exp(-x2)h=b-an=1-010=0.10 table for x and y values x 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1…

Q: (a) Estimate | V1- x² dx using the left end points of 4 equal intervals. (b) Knowing that the…

A: We have to find the approximation and value of integral.

Q: What is the value of df rez+1 (0), where f(x)= da 1+e-z Give your answer as an integer or as a…

A: Brief answer is given below.

Q: 3 Approximate dx using 6 rectangles. +2 It is approximatley. (Round final answer to 3 decimal…

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Q: e Tx dx x2 e 3. S

A: We are asked to evaluate the integral.

Q: The integral / sin²xcos?xdx is equal to M – cosN) dx' what is M and N? (1- M= N=

A:

Q: Calculate the left rectangle approximation of - using five subintervals. dx L5 = 1.260 O L5 = 0.746…

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Q: L (21 +x+3)dx

A:

Q: Q2/Find the value of the integral ²: by using simpson method (n = 6)? dx 1+x²

A: Let's solve given integration by using simpson 1/3 method.

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.