4. Use residues to evaluate the improper integral 1t r4 a + x2 dx; where a is a real constant.

Q: Evaluate the iterated integral. 8 4 b²b²x + (x + y) dy dx

A: Given query is to find the value of the integral.

Q: Еxercise: 1- Use the Composite Trapezoidal rule with the indicated values of n to approximate the…

A:

Q: Find the Particular Integral for the given differential equatiorn d²y dy +3- dx +6y =2x²+x+5 dx2…

A: using expansion,         (1+x)-1 =1-x+x2 -x3+...

Q: b) Calculate the following integrals x²(3x³ + 2)²dx (i) (ii) sin3x e³x dx (ii) (2x22+₁ +*²+2) dx S…

A:

Q: Evaluate the iterated integral. 8. 15 (x + y²) dx dy

A: When integrating with respect to one variable, consider other variable as constant.

Q: 2. Suppose | 29(r)dr = 10. Using linearity properties of integrals, calculate | (g(x) + 3)dx. 3

A:

Q: 1 Suppose we perform the substitution u=3+Vx in the integral dx . I (3+ Vx)4 What is the resulting…

A: we have to find the given integral

Q: 1. Approximately compute the value of the following integral, as accurately as possible, using the…

A: Note:- Here, you mention function f(x) is creating little bit confusion for me. Is…

Q: 4 4y Evaluate the iterated integral хуdxdy. y

A: The objective is to evaluate the integral ∫04∫y4yxydxdy .

Q: Evaluate the iterated integral: 2 sin(xy) dy dx п/2 1

A:

Q: 3 2 Evaluate the iterated integral x cos y dy dx. 2 3л 2

A: Ans= 5/2=2.5 For detail go through the solution...I have solved step by step in detail

Q: Calculate the double integral 2 dædy D= {(x, y)| 3< ¤ < 5, 5 –¤ < y < 8 –x} D x3 Enter the exact…

A: We need to evaluate double integral.

Q: 1. Find a particular integral for d²y dy dr +4- + 3y = r? dr2

A:

Q: 3 The triple integral L (x + 2y – z)dxdydz is equal to

A:

Q: 1. Evaluate the improper integral or show that it diverges. (a)/ e* dx 8. (b) / dx (c) d.r (d) /…

A: If the limit exists and is a finite number , we say that the improper integral converges .If the…

Q: Evaluate the iterated integral. (x² – y²) dy dx -1J-4

A:

Q: 1. Find the integral of f xe¯*dx using Trapezoidal with Romberg with k = 3.

A:

Q: Evaluate the iterated integral. 8 3 (x + y²) dx dy -1/1

A:

Q: 8. Depending on the real parameter p and q, what can you say about the result of the following im-…

A:

Q: Evaluate the iterated integral. 4 (x² – 2y²) dx dy %3D

A: We need to evaluate the following integral ∫12∫04x2-2y2dx dy

Q: (a) Calculate the iterated integral 3 7/2 SS(v+y° cos x)dx dy -3 0

A:

Q: 4. Use the substitution formula and evaluate the following integral: dy -1 y/4y² – 1

A: This question is based on the substitution, make a substitution for y such that the denominator part…

Q: C for the con

A:

Q: Evaluate the iterated integral. (x² – y²) dy dx -1J-2

A:

Q: 2. Approximate the following integrals using Gaussian quadrature with n = 1 and n = 2. 1 а) -dx x² –…

A:

Q: Evaluate the iterated integral. 4 5 6 (x² + y² + z²) dx dy dz -4 0 0 5 6 (x + y? + 2? )dx dy dz = i…

A:

Q: 5. Evaluate the iterated integrals. a. b. [²³² (x+y)dx dy S S S xyz dx dy dz

A:

Q: Evaluate the iterated integral. *7/3 '5 y cos(x) dy dx

A:

Q: evaluate the iterated integral.

A: Given, ∫-12∫0π2ysinxdx dy Now integrate above with respect to the x we get, ∫-12∫0π2ysinxdx…

Q: 3 The integral ³³ g(x, y) dxdy is equivalent 3 to ₁ ³x g(x, y) dydx

A:

Q: Evaluate the iterated double integral: x+4 sin (y – 3y?) dy d.x x+4

A:

Q: S For x1/2 x−x³ dx and using the substitution u=x1/2, the resulting integral takes the form:

A:

Q: Evaluate the iterated integral. 3 4 5 /// + x² + z² ) dx dy dz -3 0 0 3 4 5 !! (x² + y² + z² )dx dy…

A: We have to find

Q: Depending on the real parameter p and q, what can you say about the result of the following im-…

A:

Q: Evaluate the improper integral A 0 (B 4 C diverges 2 D 9 mit 2 3 -2 X 3 dx

A:

Q: ...... ... ... ...- Evaluate the iterated integral. 5. y cos(x) dy dx

A:

Q: Evaluate the iterated double integral: x+4 sin (y³ – 3y?) dy d.x - x+4

A: Let's find.

Q: Evaluate the integral x2 ds where C is the portion of x2+y2=4 from (0,2) to (-2,0).

A: ANSWER:

Q: Evaluate the iterated integral. 2y 1²1,²% (10 + 8x² + 6y²) dx d 0 ly

A:

Q: 1. Evaluate the integral Vi-x² ex?+y*dydx.

A: 1. The given integral is, ∫01∫01-x2ex2+y2dydx. Convert the integral into polar coordinates as…

Q: 2. Approximate the following integrals using Gaussian quadrature with n = 1 and n = 2. 1 1 2 -dx 4…

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: 1. Use Numerical methods to approximate the following integrals (a) (x +y)dxdy , n = m = 3

A: Trapezoidal rule: ∫cd∫abf(x, y)dxdy=h2fa, y+2fa+h, y+fa+2h, y+⋯+fa+n-1h, y+fb, ydy, where h=b-an.…

Q: Evaluate the exact value of the multiple integral. 2 In 2z c2y e*dx dy dz 2 Jinz -y

A: This question is related to definite integration, we will solve it solve it using given information.…

Q: Evaluate the iterated integral. 3 4 5 | /| (x² + y² + z²) dx dy dz -3 0 0 3 5 (x² + y? +z? ?)dx dy…

A: Application of integration

Q: 2 Evaluate the iterated integrals. 2 (x + 3) dy dx 0, 6. y sin x dy dx

A:

Q: /4 1.* Use the following property of the definite integral to estimate the definite integral:JCcos x…

A:

Q: Evaluate the iterated integral. (x² – y²) dy dx J-4

A: Given the double integrationI=∫−11∫−44(x2−y2)dydx

Q: Evaluate the iterated integral. 16 - y2 4 (x + y) dx dy

A:

Q: Evaluate the iterated integral. 2 4 (x2 – 2y2) dx dy 1 Jo

A:

Arc Length

Arc length can be thought of as the distance you would travel if you walked along the path of a curve. Arc length is used in a wide range of real applications. We might be interested in knowing how far a rocket travels if it is launched along a parabolic path. Alternatively, if a curve on a map represents a road, we might want to know how far we need to drive to get to our destination. The distance between two points along a curve is known as arc length. 

Line Integral

A line integral is one of the important topics that are discussed in the calculus syllabus. When we have a function that we want to integrate, and we evaluate the function alongside a curve, we define it as a line integral. Evaluation of a function along a curve is very important in mathematics. Usually, by a line integral, we compute the area of the function along the curve. This integral is also known as curvilinear, curve, or path integral in short. If line integrals are to be calculated in the complex plane, then the term contour integral can be used as well.     

Triple Integral

Examples: