a) 1+x? dx approximate the integral for 1, 2 and 4 intervals with Simpson's method. b) 1+x2 dx Approximate the integral both directly and by trapezoidal method for intervals 2 and 4.

Q: 10. Prove by using integration by change in variable the ff. integral: dx :du 3D arcsecх+ С xVx2 – 1

A: We have given the integral ∫dxxx2-1 = I(say)     Put   x2-1 = t   ⇒x2= t2+1     Differentiate w.r.t…

Q: (b) Find a value for n to ensure that the absolute error in approximating the integral xsin x dx by…

A:

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: (3, 1) (у? + 2ху) dx + (- 1, 2) (x² 2ху) dy +

A: We have to show that the curvilinear integral is independent of path and we have to find its…

Q: Use the tabular method to evaluate the integral - 2x – 1) cos(4x)dx

A: Introduction: Tabular integration is a technique for quickly integrating many parts in a row. One of…

Q: 1- Use trapezium's Rule with n = 4 to approximate the integral Vx dx

A: We have to use formula of Trapezoid Rule.

Q: •3 Evaluate the integral / | 0. dx dy by reversing the order of integration. NOTE: Enter the exact…

A: This question is related to double integral, We will solve it using given information.

Q: 2 Find the definite integral o tan(x)dx using strips of width for the trapezium rule correct to…

A:

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

A:

Q: Using appropriate substitution, the integral *+imx) dx is equal to: an

A: From the given problem:   I=∫141+lnx3xdx...1   Substitute in equation (1).   1+lnx=u...Differentiate…

Q: 3. Solve the integral by two grid in the y-direction and four grid in the x-direction with…

A: Solve the integral by two grids in the y axis and four grids in the x axis with Trapezoidal rule:…

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

A:

Q: The integral dx is improper for two reasons: The interval [0, co) is infinite and the integrand has…

A:

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: Consider the integral Í dx . For which value of n the error in trapezoidal rule will be less than…

A:

Q: Consider the curve segments: 1 $1: y = x² from x =to x = 3 and 3 1 52: y = Vx from x =to x = 9. Set…

A:

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

A: Solved below

Q: 10. Prove by using integration by change in variable the ff. integral: dx du = arcsec x + C xVx2 - 1

A: To show∫dxxx2-1=sec-1x+C.

Q: Use (a) the Trapezoidal Rule and (b) the Midpoint Rule with n=5 toapproximate the integral  integral…

A:

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: In using the technique of integration by parts, you must carefully choose which expression is u. For…

A:

Q: Evaluate double integral 0 to 2, x to 2 2y^2 sinxy dydx

A: We have to integrate the double integral:

Q: Calculate the integral approximations Tb and Mb for sec x dx %3D

A:

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

A:

Q: Evaluate the integral / (2x + 12y)dx + (24x – y)dy along the parabo arc y = x² from (0,0) to (1, 1).…

A: Solution is below

Q: Consider the improper integral: x² +2x+2 dx what will be the appropriate solution and answer? A Im…

A: ∫0∞1x2+2x+2dx

Q: Given that x2 dx use this fact and the properties of integrals to evaluate (2 - 3x2) dx. %3D

A: Answer is- 1 Explanation is given below...

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

A:

Q: Find the trigonometric integral. (Use C for the constant of integration.) sin(x) cos os°(x) dx

A:

Q: Evaluate the integral (8 (8x+15y)dx + (27x - y)dy along the parabolic arc y = x² from (0,0) to…

A:

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

A:

Q: To find the arclength of y = 3x² + 3 from æ = 0 to x = 4, which is the correct integral? OL = | VI+…

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: Evaluate the integral - T/2 (8 + 4cosx)dx 0. Using:

A: The given integral is ∫0π28+4cosxdx In part (a), we shall solve it analytically, and in part (b), we…

Q: (b) 3 – cos(x) 2

A: Follow the procedure given below.

Q: * Using integration by parts, the integral sec³dx is equal to 1 1 - secxtanx +In|secx +tanx| + C 2 1…

A: Use by parts method of integration

Q: 2. Use the error formula to estimate the error in approximating the integral T/2 2 sin x dx using…

A:

Q: Approximate the integral S" x² sin x dx by Trapezoidal rule with n = 4. O Find the minimum n…

A:

Q: Use (a) the Trapezoidal Rule integral 1to 4    sin x dx                 with n= 5

A:

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

A: ii)  Equation is f(x)=exp(-x2).The value of the table for x and y x 0 0.25 0.5 0.75 1 y 1…

Q: 3.a) Apply the Trapezoid and corrected trapezoid rule, with h =, to approximate the integral £mcx+…

A:

Q: 2 Find the definite integral o tan(x)dx using strips of width for the trapezium rule correct to…

A:

Q: Compute the defined integral So [1+ e* sin(4x)] dx using the trapezoidal method with two segments.…

A:

Q: 3. Approximate the integral using: (a) (b) 11 trapezoidal rule. Simpson's rule. 0.8 [8 dx

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: Consider the integral dx . For which value of n the error in trapezoidal rule will be less than…

A:

Q: Find the trigonometric integral. (Use C for the constant of integration.) tan (x) dx sec (x) c^(x)

A: To Evaluate: ∫tan3xsec4xdx

Q: (b) Using the Trapezoidal rule with four strips (intervals), estimate the integral | sin (r/2) dr .…

A:

Q: Consider the curve segments: S1: y = r from x = to x = 4 and !! S2: y = Va from x=- to x = 16. Set…

A:

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.