2² + e4 z lim z 0 22 – e²

Q: Show that the following line integral is path independent and evaluate its value. Show the details…

A:

Q: ) Use integration by parts to verify the reduction cosxsin x n-1 Scos" xdx=!

A: Here I=∫cosndx ⇒I=∫cosn-1x×cosx dx using integration by part;

Q: b) Estimate the integral esindx using composite traperoidal rule with h= 0.25.

A:

Q: Prove That:- o sinhz= loy (Z+lz*+l )

A: To prove, sinh-1z=logz+z2+1     Lets consider, y=sinh-1z…

Q: Illustrate the setting up limits of a double integral?

A:

Q: Define stpes to obtain the general solution of a 2nd order homogeneous ODE with real coincident…

A:

Q: Show that the following line integral is path independent and evaluate its value. Show the details…

A: If line Integral is path independent then there exist a function which is called potential function

Q: Сompute L f dx, where f(x)=|x|.

A:

Q: Verify Green's Theorem by evaluating both integrals aN dA |v² dx + - x² dy ax ду for the given path.…

A:

Q: Find the integral m tanx X, 1+x?

A: Given :

Q: Queston} $²3 20c x²-4 Composite Trapezoidal rule with n=4 dx. 3.1.1. use the to approximate…

A:

Q: Use integration by parts to prove the reductionformula.

A: Consider the following integration by parts formula: ∫uvdx=u∫vdx-∫dudx∫vdxdx ILATE Rule: We have two…

Q: Evaluate the integral. 1//3 3earctan(y) dy -V3 1 + y2

A:

Q: (1,2) (b) Set up a definite integral that is equal to the arc length of the portion of the circle…

A: Note:- As per your request i am solving here question no. 3 part B only.

Q: Evaluate the improper intergal 1 dx using the residue (x² + 16)² theorem.

A: We need to evaluate integral.

Q: 5) Set the iterated double integral ļ) dydx メモービ テ as Jady up

A: Please see the below explanation.

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: y = sech*x = In(_+ V1- x², sechx = In(- 1+ V1-x² Prove that .... ..

A:

Q: Calculate the integral: /3 arctan(x) dr a) O 3x arctan x – In(1 + x²) + C b) O3 In | arccos x| + C…

A: we will apply the integration by parts rule: ∫(u·v) dx=u∫v dx−∫u'∫v dxdx And we also use…

Q: Queston Ser x²-4 Composite Trapezoidal rule with n=4 3.1.1. use the to approximate integral. 3.1.2.…

A: Note:- For part (2), you don't mention method name so, i assume it Trapezoidal rule with n=3. If you…

Q: Solve the equation by Cauchy's integral theorem. 1- dz 2- . 2z(4– z)dz

A: Hello. Since your question has multiple parts, we will solve the first part for you. If you want…

Q: Compute the point of intersection of the curve sinx and x-1 with the help of Bisection method. Ans.…

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

Q: Find the integration of S ecosx dx using Trapezoidal and Simpson's Rules

A:

Q: 4. Use the definition of integration to find (1+2x' ) dx , that is find lim f(x; )Ax

A:

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

A:

Q: Evaluate the integral f 2x ¡dx using the two-point Gaussian quadrature rule. 16 \\frac{2}{3}\)

A: Given integral is ∫−222x216+x4dx. We have to evaluate the given integral using the two-point…

Q: Show that the following line integral is path independent and evaluate its value. Show the details…

A: Step:-1 Note:- 1. ∫∇F.dr =∫fx i +fy j dx i +dy j  2. Fundamental Theorem of Calculus:- ∫bc F'(x) dx…

Q: integral from -1 to 1 of arccos (y) dy

A:

Q: 7. Use the Fundamental Theorem of Line Integrals to evaluate S(6xy, 3x² + 6y²) · dr where C is any…

A: Line integral theorem

Q: Set up UP the integrel the Pegioni Th bounded 2x2 and y =l+ x F(x,y) dA in by: y= 2x? 2. 4.

A:

Q: plot Y funetion of as over Hhe Peenge ☺.0l <*< l00.

A:

Q: (5)Obtain the integral curve for x 2+y = x passing through the point

A:

Q: Show that the integral is independent of the path, and use th Fundamental Theorem of Line Integrals…

A:

Q: Find the integral of * dx J 2 sin x – cos x tan + 2 + V5 + C tan+ 2- V5 V5 |tan + 2-V5 V5 In tan+ 2+…

A: Option 2 will be correct choice.

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

A:

Q: Find the are length of the curve y² = 3x between the from x=0 to x=9 ! Use integral approximation!…

A:

Q: nsi Sinhna (na)? 8. ) Sind( x) Sin y)

A: Given Fourier series, ux,y=∑n=1∞1sinhnπ8sinnπ2nπ2sinnπ2sinhnπy2+8nπ2-8cosnπnπ2sinnπx2sinhnπy2 To…

Q: Find the Selution of (1-t +3t)4 (t) di - , (2) In which IL) denoter Bessel function

A: Leibniz integral rule : ddx∫bxaxFtdt=∫bxax∂∂xFtdt+Faxddxax-Fbxddxbx   Linear Volterra Equation of…

Q: 64 ans: su 3 6. Calculate the area between the Curve fcx) = x²³²_4 and the lines y=2x + 4 and y=0,…

A: area between curve

Q: Evaluate the improper intergal dx using the residue 2 (x² + 4)² theorem.

A:

Q: Let f(x) = (cosh x)² be defined on (0, 0), find %3D d 1/2) . dy

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

A:

Q: Evaluate the in tegral (x+ 2y) dy

A:

Q: 2. Determine the values of ʼn and h required to approximate fx²sin (-x) dx to within 10% using the…

A:

Q: Compute the integral ∮C [(cos x − 3y) dx + (2x − sin y) dy], where C is the closed curve that…

A: The region of integration C is divided into three line segments C1, C2 and C3. Let C1:y=0,…

Q: isolated singular point 1. z/((z^3)+z) 2. exp(tan(1/z)) 3. (1/(z^2)) * exp(1/(z^2)) z=4 is apole of…

A:

Q: Use the calculus of residues to evaluate the improper integral COSX -dx. (x²+1)³

A:

Q: et * e-t Compute the convolution integral.

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.