Use the composite trapezoidal and Simpson's rules with step length h = 0.4 to estimate In(2+3/x) -dx, 1+x² and compare your result with the result I = 0.59655, which is correct to five decimal places.

Q: Use the midpoint rule with n = 6 to estimate the value of the integral (x³ + x)dx.

A: Given integral is ∫03 x3+xdx Number of sub-intervals = 6 Take f(x) = x3+x Step size  ∆x  = 3-06…

Q: 2. Using both trapezoidal and Simpson rule, find the approximate values for the integral S7 n = 20…

A: we nee to find ∫π4π2ln(tanx)dx,  n=20 a=π4=0.7854,  b=π2=1.5708 ,  y=ln(tanx)…

Q: Use the midpoint rule with n = 6 to estimate the value of the integral (x³ + x) dx.

A:

Q: The following problem is for extra practice and does not have to be submitted. 2 1 -dx using the…

A: According to question ∫0211+x3dx,       n=4

Q: Evaluate dy/dx at x = 2.5, correct to 3 significant figures, given y= (2x^2+3)/In 2x

A:

Q: Use the Trapezoidal Rule and Simpson's Rule with four subintervals to estimate x* dx.

A: Trapezoidal Rule

Q: 2. Use the composite trapezoidal rule with the step length h = 0.1 to evaluate dx I = 1+x2 and…

A: Composite trapezoidal and composite Simpsons 1/3rd rule

Q: Estimate | (2x – 5) dx using left endpoints for n = 3 approximating rectangles. %3D 5 (2x – 5) dx is…

A: Given: ∫152x-5ddx The left Riemann sum (also known as the left endpoint approximation) uses the left…

Q: How large should we take in order to guarantee that the Trapezoidaland Midpoint Rule approximations…

A: Given

Q: S(1 - In =) 1 dx x2

A:

Q: The error is numerically computing the integral | 1 dx using the +4 trapezoidal rule with two…

A:

Q: Use the midpoint rule with n = 6 to estimate the value of the integral (x3 +x)dx

A:

Q: Use the Trapezoidal Rule to estimate the integral |dx using n = 4. What n is needed for 2 decimals…

A:

Q: The approximated value of the integral fe* dx is equal to - Rule with step size (h=2). when using…

A:

Q: (a) Use the Midpoint Rule with n = 6 to approximate integral S³ dx 8 x-6 6 x+8

A: Multiple questions-"As per our guidelines we are suppose to answer only one question.Kindly re-post…

Q: Use the midpoint rule with n = 6 to estimate the value of the integral (x³ + x)dx

A: We need to use the mid-point rule to find the value of the definite integral.  The mid-point rule…

Q: Use the Midpoint Rule with the given value of n to approximate the integral. Round the answer to…

A:

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

A: Given integral is ∫021+x3dx and h=1. We have to approximate the given integral by using Simpson's…

Q: 2 By using Trapezoidal rule, the value of "h" in evaluating - 2x + 6)dx , by taking 10 subintervals…

A: Solved below

Q: Use the Midpoint Rule with n = 4 to approximate 2x the integral 1 dx to three decimal place.

A:

Q: Use Romberg's method to compute dx 1+x? correct to 4 decimal places by taking h= 0.5,0.25 and 0.125.

A: AS PER OUR GUIDELINE WE ARE SUPPOSED TO ANSWER ONLY ONE QUESTION. KINDLY REPOST OTHER QUESTION AS…

Q: (a) Use the Midpoint Rule with n = 6 to approximate integral 8 x-6 S8 dx 6 x+8 ?

A: As per the instruction, we will be answering the first question. Given:

Q: Q3] Use the trapezoidal rule of integration to determine the value of S, xlnx dx with h = 0.1, work…

A:

Q: Use integration by parts to prove the reductionformula.

A: We have to prove the reduction formula using integration by parts method: ∫xnexdx=xnex-n∫xn-1exdx If…

Q: Evaluate the following integration: 3x-2)dx Using trapezoidal rule for 100 and 1000 equal segments.

A: Given integration is ∫02x5+3x3-2dx Solution a: let f(x)=x5+3x3-2 Using Trapezoidal rule Here equal…

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

A:

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

A:

Q: Use Simpson's Rule with n = 4 steps to estimate the integral. 42) | 7 dx 1+X

A:

Q: Use Simpson's Rule with n = 4 steps to estimate the integral. dx O 18 O 15 36

A: Given:    f(x) = x  Limit: 0 to 6    n = 4

Q: Use the Trapezoidal Rule with n = 6 to ex approximate dx | 1 х Use the Simpson's Rule with n = 6 to…

A:

Q: Use the Midpoint Rule to approximate the integral 13 | (- 2x + 10æ²) dx with n=3.

A:

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

A:

Q: MY N nd the minimum value of n that guarantees an error of no more than 1/30,000 in approximating -…

A:

Q: Using the trapezoidal rule with n = 5, approximate the integral L' TO S³ give the error of…

A: Trapezoidal rule formula: ∫abf(x) dx=h2(y0+yn)+2(y1+y2+...+yn-1) Given ∫03dx16+x2 Here f(x)=116+x2…

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

A:

Q: 4) Use the Trapezoid Rule and Simpson's Rule with n 6 to estimate Vx dx

A: Trapezoid Rule: ∫abf(x)dx=∆x2fx0+2fx1+2fx2+.........+2fxn-1+fxn                        where,…

Q: Calculate an approximate value of the integral x2 dx by dividing the 1+x interval into 4 equal parts…

A: In the question we have to find the value of integral by using Simpson's one - third rule.

Q: Evaluate e" dydx by reversing the order of integration. x/3)

A: A detailed solution is given below.

Q: Use the Midpoint Rule with n = 4 to approximate the integral. 10 x² dx M4 =

A: The given integral is ∫210x2dx. The mid point rule states that if fxis continuous on [a,b][. Let n…

Q: Use the Simpson's rule to estimate e**dx with n = 4

A:

Q: Find the minimum value of n that guarantees an error of no more than 1/30,000 in approximating the…

A: Given the integral: Hence we have

Q: 7) Estimate the value of e dx using Simpson's rule using 8 subintervals.

A: Given: ∫02ex2dx Here, n = 8 subintervals

Q: : Evaluate fxe dx to using Romberg integration to an error of order

A:

Q: Use the Midpoint Rule with n = 4 to approximate the integral. %3D 14 x2 dx

A: We have to solve the integration using mid point rule.

Q: 5) Approximate -dx 1 +: Using the Trapezoidal rule and Simpson's rule with h=1. Find an error in…

A: We have to use both numerical methods for 4 subintervals as h=1 and (b-a)=4.

Q: Use integration by parts for both.

A: The given integral is

Q: 3. Estimate the value of the integral 1 dx (n = 4) using Trapezoidal rule. 1+ln x

A: The value of h in the trapezoidal rule is h = b-anh = 5-34h = 24h = 0.5 Form a table with the x…

Q: use the midpoint rule n=5 to approximate  integral 1 to 2 (1/x) dx

A: To find: The approximate integral of ∫121xdx with mid point rule n=5. Concept used: If fx is…

Q: Solve numerically the integral e**dx ´dx by: (1) Trapezoidal rule with n = 4 (ii) Simpson's rule…

A: The given integral is, 12π∫-22e-x2dx

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…