•5 Evaluate | Vx+ e¤ dx using the midpoint rule with 5 strips, giving your answer to 2 decimal place. The midpoint rule for estimating the integral of y = f(x) can be stated as y dx = h (yi +. + Yn), - a where h and y; = f(x;). n

Q: Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule to approximate the given integral…

A:

Q: Evaluate the line integral -ydx + xdy along the curve C: y? = Зх from (3,3) to (0,0). NOTE: Enter…

A:

Q: Q.2 Find area under the curve y = x² +1 over the interval [0,3], Using Riemann sum.

A:

Q: f lim f(x) = o then | f(x) dx is an improper integral.

A: True As f(x) tends to infinity when x goes to b This will make function improper

Q: ite the integral (Use C for the constant Integration) In Vx)dx

A:

Q: Q3/Find the value of integral along the curve C joining the points (1, 1) and (2, 3) | (12z2 – 4iz)…

A: We have to find the value of integralalong the curve C joining thepoints (1, 1) and (2, 3).

Q: -1 -1 Differentiate xe 1 2 and hence integrate 2 dx.

A: Let g(x) =x e-12 x2 then x -derivative of g is given by dgdx=ddxx e-12 x2  now , using product rule…

Q: ii. In(x) dx

A: Using integration by parts,

Q: Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule to approximate the given integral…

A:

Q: 2. Triple Integrals For any continuous function f and constant a > 0, show that cx 1 II Fl0) dz dy…

A: Just integrate one by one.

Q: Find the work integral of F = ⟨y^2, x⟩ along the line segment C starting from P(0, 1) and ending at…

A:

Q: x TC Q2\ Find The Area under the curve Y= 4sine between X= and 2 X= π by the double integral method.…

A: Let's find area by using double integral method. Small mistake in given question, there should by…

Q: y + 2 "hat is the indefinite integral of JC² - 1)(² + 1 )" dy ? 2 (y² – 1) (x² + 1

A:

Q: 5b. Consider the function y = v9 – x² from x=-2 to x = 2. Set up an integral for the surface area…

A:

Q: Find the area between these two curves (use substitution method to solve integral) x = \yl V1 – y² &…

A: Explanation of the answer is as follows

Q: Evaluate the double integral: y SLAZ+1 y²/3 x + 1 (Hint: Change the order of integration to dy dr.)…

A:

Q: Sr 'dx integralini Trapezoidal yöntemini kullanarak yaklaşık olarak hesaplayınız. Use the…

A: To evaluate the given integral using Trapezoidal rule.

Q: Find the area enclosed by the curve x = t2 - 4t, y = -Vt and the y-axis. A = S rdy or A= S. (TR-IL)…

A: x=t2-4t, y=-ty=0 →t=0y=-2 →t=40≤t≤4dydt=-12t

Q: The region bounded by the curves f(x) = 1 – (x – 1)² and g(x) = (x – 2)² – 4 is revolved about the…

A:

Q: xy Does there exist a positive number a such that the double integral over the rectangle defined by…

A:

Q: y3 Set up an integral that represents the surface area of the surface generated by revolving the…

A:

Q: Ris the region bounded by the following graphs: A1:y = /25 – x² x2 A2:y =7 %3D - 2 Аз:у %3 2х — 5…

A: Washer Method to find the Volume of the solid that revolving about the line y=5.

Q: f(z)dz what are the bounds of integration for the first integral? a = and b =

A:

Q: Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule to approximate the given integral…

A: Given : The integral  ∫12x3-1   dx   , n = 10   To determine : The value of the integral using (a)…

Q: Q4) Use a double integral to find the area of the region R enclosed between the parabola and the…

A: To find the area of the region R enclosed between the parabola and the given line. Since the…

Q: c. Integrate the function f(x, y) = x-y over the triangle with vertices (0,0), (1,0), and (2, 1). Do…

A:

Q: Q5/ change the cartesian integral in an equvalant polor integral then evalute 2x-x² the polor…

A:

Q: Evaluate the double integral I3 = SS (22-2 3) dxdy where S is the region in the 4th quadrant (y < 0,…

A:

Q: A cormpany manufactures mountain bikes. The research department produced the marginal cost function…

A: Evaluate the increase in cost

Q: Set up an integral for the length of the curve. y = x°,0< xs 1 1 V1 + 6x5 dx V1 + 6x10 dx V1+ 36x10…

A:

Q: Evaluate the integral by reversing the order of integration. 16 2 y3 dy dx + 1

A: Answer and explanation is given below

Q: 4-x2 xe?y dy d.r, 4 - y Sketch the region of integration C, reverse the order of integration, and…

A: First I have see the limit of integration for x and y and then draw the region and then taking strip…

Q: E valuate the area bounded by the parabola the Parabola X= y omd integral X = 2y-y using double

A: Please see the graph below to first understand what's going on:

Q: dz z(z – 2)4

A:

Q: 3 In(x3 + 7) dx, 4 n = 10 (a) the Trapezoidal Rule (b) the Midpoint Rule (c) Simpson's Rule

A:

Q: integral of F(x) =e3x dx. on the interval [0, ln3]

A:

Q: Q1) () points) a) Sketch the region of D = {(x,y) :-√√4-y≤x≤ ¹,0 ≤ y ≤ 4} b) Reverse the order of…

A:

Q: You are rotating the region bounded by y 2 = x, y = 1, and x = 0 about the line x = 1. Set up the…

A: First, we sketch the region using a graphing calculator  y2=x , y=1 , x=0 The shaded region is…

Q: triple integral of  3xy dV, where E lies under the plane z = 1 + x + y and above the region in the…

A: Let's find.

Q: V2-x2 Q) Sketch the region of integration for the integral L* dydx and evaluate the integral with…

A:

Q: Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule to approximate the given integral…

A: Solve the following

Q: Q1/ Set up the limits of integration for evaluating the triple integral of a function F(x, y, 2) (0,…

A: NOTE:- AS POSTED MULTIPLE INDEPENDENT QUESTIONS, WE ARE ANSWERING ONLY FIRST QUESTION AS PER…

Q: Integration review Evaluate the following integrals.

A: We have to evaluate the integral: ∫π6π2dysin y Applying identity cosec x sin x=1⇒cosec x=1sin x, we…

Q: integrals in the order dædzdy 11 x2 1 | s(e;y, z)dydzdr

A: Please refer to the image below

Q: sketch the region and evaluate the integral by changing the order of integration 22-x || (x+ y) dy…

A: part(a):   The given limit are changing from y from 0 to 2 – x and x from 0 to 2.   Sketch the…

Q: Evaluate the line integral -ydx + xdy along the curve C : y = 3x from (3, 3) to (0,0). NOTE: Enter…

A: We have to find the line integral ∫C-ydx+xdy along the curve C: y2=3x from (3,3) to (0,0)

Q: Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule to approximate the given integral…

A: a) Trapezoidal Rule: First, evaluate the value of delta(x).

Q: Calculate the double integral. - 15y4) dA , R = {(x, y)|0 <x < 3,0 < y< 1} The value of integral is

A: dA = dx * dy

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.