1 1 dx exactly and show that the result is Evaluate 1+ x? Then, find the approximate value of the 4 integral using the trapezoidal rule with n = 5 subdivisions. Use the result to approximate the value of 7 . The approximate value of 7 is: Give your answer accurate to four decimal places. Question Help: D Video 1 Video 2

Q: Q4 dx Q4: Apply Simpson's rule to find the approximate value of the integral with h =! (8 marks)

A:

Q: |x| dx find the value of the integral and specify the which improper integral it is. -1 V1 – x²

A:

Q: 1 1 dx exactly and show that the result is Evaluate Then, find the approximate value of the 4 1+ x2…

A:

Q: 1 -dx exactly and show that the result is Evaluate Then, find the approximate value of the 4 1+ x2…

A: We have to find  the exact value of integral, approximate value of integral using trapezoidal…

Q: Evaluate the integral using an appropriate substitution. NOTE: Enter the exact answer. 9e dx 1+e2=…

A:

Q: Use the Table of Integrals to evaluate the integral. (Remember to use absolute values where…

A:

Q: V4 Evaluate the integral: dr 3x2 (A) Which trig substitution is correct for this integral? Ox = 2…

A:

Q: dx Evaluate the integral: 49 (A) Which trig substitution is correct for this integral? 49 sec(0) 16…

A: Here remember the trigonometric integral formula and proceed as follow.

Q: 1 dx J Vx² + 2x + 5

A:

Q: 20x² Evaluate the integral: -dx V64 – 72 (A) Which trig substitution is correct for this integral? 8…

A: Given, I=∫20x264-x2dx To Evaluate (A), (B), (C), (D)

Q: 1 dx exactly and show that the result is Evaluate 1+ x² . Then, find the approximate value of the 4…

A: The exact integral is: ∫0111+x2dx=tan-1(x)01=tan-1(1)-tan-1(0)=π4-0=π4

Q: 7. Approximate the value of the given integral by compieting parts (a) and (b) below. (a) Use the…

A:

Q: Evaluate the improper integral or show that it diverges. 6 S dx 0 √36-x² Select the correct choice…

A: Explanation of the answer is as follows

Q: I = ₁e²+¹dx_ Divide the integral into 5 equal parts (n=5) and obtain the numerical integral with the…

A: Given: integral is ∫24ex2+1dx and n=5 To Find : The numerical integral using Trapezoidal Method  and…

Q: 40 (a) Evaluate the integral: / da x² + 4 Your answer should be in the form kn, where k is an…

A: (a) Given integral : ∫0240x2+4 The integral can be further written by separating the constant as…

Q: dx exactly and show that the result is Evaluate 1+ x2 (Hint: substitute x = tan u.) 4 Then, find the…

A:

Q: O Po Find the indicated trapezoid approximations to the following integral. 10 4x dx using n= 2, 4,…

A: Given integral can be evaluated by using trapezoidal approximation at n=2,n=4,n=8 sub intervals as…

Q: Use n= 4 to approximate the value of the integral by the following methods: (a) the trapezoidal…

A: The given integral is 5/x2 limit from 1 to 4.

Q: dx 3. Evaluate the integral I = Include 4 decimal places on your computation. +6x+10 b. multiple…

A:

Q: Given the integral S. 2+cost dt . i. State whether the trapezoidal rule can be used to approximate…

A:

Q: I = √²+¹dx Divide the integral into 5 equal parts (n=5) and obtain the numerical integral with the…

A: Trapezoidal rule: ∫abydx=h2(y0+2(y1+y2+y3+...+yn-1)+yn)  to approximate the integral: ∫abydx. Here,…

Q: Convert the line integral to an ordinary integral with respect to the parameter and evaluate it. (y…

A:

Q: Convert the line integral to an ordinary integral with respect to the parameter and evaluate it. lo-…

A: Use parametric to solve

Q: nd the integral (z + 1)e7² dz. (z + 1)e²² dz

A:

Q: Consider the definite integral given below 3.5 S (x cos (3 z) - 1.1 z³) dz 0.1 a) What is the value…

A:

Q: 0.5 b3 a where a <b, to evaluate the integral s ds. Use the fact that a 0.5 The value of the…

A:

Q: 48 (a) Evaluate the integral: dx x² + 4 Your answer should be in the form ka, where k is an integer.…

A: (a) Given information: ∫0248x2+4dx

Q: Evaluate 1+ g² dz exactly and show that the result is Then, find the approximate 4. value of the…

A:

Q: Using a Table of Integrals with the appropriate substitution, find + 5e" dx e2 - 100 se3x + 6e2x…

A:

Q: 3. DETAILS Consider the following integral 3d.x V(16 + 4x2)5 A suitable trigonometric substitution…

A:

Q: Use n = 4 to approximate the value of the integral by the following methods: (a) the trapezoidal…

A:

Q: (29/x2 Evaluate the integral: -dx (A) Which trig substitution is correct for this integral? O x = 2…

A: To evaluate the integral: ∫29x2-4x4 dxA To determine which trig substitution is correct for this…

Q: dr Evaluate the integral: [s1 – (72)*]"* (A) Which trig substitution is correct for this integral?…

A: Given, ∫dx81-7x232

Q: Evaluate the integral using integration by parts with the indicated choices of u and dv. (Use C for…

A:

Q: 1 dx exactly and show that the result is Evaluate 1+ x2 . Then, find the approximate value of the 4…

A: Formula ∫ 1/(1+x2)dx = Tan-1(x) Trepizoidal rule I = h[f(xo)+ 2[ f(x1)+f(x2)+f(x3)....]+ f(xn)]

Q: Use n = 4 to approximate the value of the integral by the following methods: (a) the trapezoidal…

A:

Q: 1 dx exactly and show that the result is Evaluate Jo 1+2 . Then, find the approximate value of the…

A:

Q: dx Evaluate the integral: [s1 – (72)"]"² 81 - (A) Which trig substitution is correct for this…

A:

Q: Convert the line integral to an ordinary integral with respect to the parameter and evaluate it. |(y…

A:

Q: Use the specified substitution to find or evaluate the integral. (Use C for the constant of…

A:

Q: Write an integral in the form A = g(x) dx such that A expresses the area of the region between the…

A: If f(x) and g(x) are continuous function and f(x) ≥g(x) on [a,b] , then the area between the region…

Q: Given an integral c0.2 1+ x dx. (a) State whether the Simpson's rule can be used to solve the above…

A: We can solve this using Simpson rule and 2 point Gauss quadrature formulas

Q: Using appropriate substitution and taking a + 0, 3tan(ax) the integral S dx is equal to: cos² (ax)

A:

Q: For the double integral J. sin x dA, where A is the triangle in the xy-pl 2. the x-axis, the line y…

A: We have to find the following given conditions according to the given information

Q: Used Set up, but do not evaluate, an integral for the length of the curve. y = 8 cos(x), Os xs 2x dx

A:

Q: Q. Consider the integral / V 5 – 2x dx. (a) Using the trapezoidal rule with 4 subintervals, estimate…

A: fx=∫125-2xdx.

Q: Find the exact value of the integral using formulas from geometry. + 2x)dx 1 3 J(1+2x)dx =O…

A: Area of rectangle= length* breadth Area of triangle= 1/2 base * height

Q: 1 dx exactly and show that the result is Evaluate 1+ 2 . Then, find the approximate value of the 4…

A:

Q: 1. Given ,(2x3 – 20x? + 67x – 70)dx find: a. An approximation using 4 left rectangles b. An…

A: The given integral is, ∫242x3-20x2+67x-70dx Number of rectangle is n=4.

Q: 4 Væ? + 1 dæ a) Approximate the definite integral with the Trapezoid Rule and n = 6. b) Approximate…

A: Approximate the integral ∫04x2+1 dx using a) Trapezoidal rule with n=6 b) Simpson's rule with n=6

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.