Q#01: Find the complete integral of x²p? + y²q? – 4 = 0 using Charpit's method.

Q: Evaluate the integral dx by first using the substitution u = e (e - 1)(e +1) to convert the integral…

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Q: Calculate the energy coefficient from the first order if the infinite potential box is as uneasy as…

A: Given: φn=2LsinnπxLφ2=2∂Lsin2πx2L To find: Solution

Q: 2. Consider the functions: f(t)=√1+t² and g(t) = 2t Find the convolution of the two functions by…

A: We have to find convulation of given function.

Q: dæ (xº + 2)² The integral is divergent.

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Q: By the even extension method applied to the function f (x) = e¬16x, where x > 0, the value of the…

A: We have to solve given problem:

Q: T 4. Approximate the integral fo x cos xdx with n = 6 using the Composite Simp- son's rule.

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Q: The integral ₁₁x – y dxdy is equal to: Select one: 0 O2 O None of them -2

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Q: Find the complete, singular and general integrals of p3 + q3 = 27z. %3D

A: We have to find the complete, singular, and general integrals of:  p3+q3=27z

Q: From 12ty²<³dz « dy dx, which of the following is a correct partial evaluation of the definite…

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Q: The particular Integral for (D2 + 42)y = sin4x is. Yp

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Q: b) 1+x dx Approximate the integral both directly and by trapezoidal method for intervals 2 and 4.

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Q: -1.30 Find the value of the integral 100 √x dx by using simpson method (n = 6)?

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Q: Find the integral. |(2x3 - 3x2 + x – 1) dx A x² + B 6x2 - 6x + 1 + C (c) None of the above x2 - x +…

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Q: e2ix 7. Evaluate the integral p.v. J 2+1dx.

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Q: e2z Q5- The value of the integral . Sc Where C is Z =3 (Z+1)4

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Q: Find the integral |(2 + 1)e* dz. (z + 1)e²² dz +C

A: solution is given below integration by parts...

Q: Demonstrate that for the function of the type va? + x2 you use the substitution X-atane and use it…

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Q: Use Picard's method of successive approximation to solve the equation de 1+ xy, y(0) 1 at 8.1 X-0.1.

A: Given differential equation is  dydx=1+xy, y(0) = 1 To approximate the solution at x = 0.1 using…

Q: y3 (b) Solve the integral . (cx – y)dx + (2x + y)dy along the curves x = from (0,0) to (1,1)

A: The given problem is to evaluate the given contour path integral over given path x=y3.

Q: |1-y2 ху Q3. Evaluate the double integral dxdy /1– y²,

A: We have to find solutions

Q: 3 I [(e* +x² + A\dx Дх 3 0,25 1

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Q: What is the particular integral of the equation (D 2+9) y= x Cosx?

A: Use basic properties and formula, get PI of given equation.

Q: Q3:Evaluate the integrals T|(x+y+1)dxdy -1-1

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Q: Q1 (a) Evaluate the integration of the following functions: (iii) | (3x3 – 2x 2+1)sinh 2x dx by…

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Q: 3 (e* + a² + 2) dæ x Calculate the integral with the Trapezoidal method. Take n = 8 (A =x 0.25) for…

A: See the attachment

Q: 20x 1. Given the integral J = [ (v² – w*y² )e²«*dx. %3D Find y(x) such that the integral J has a…

A: The function f(x) is a rule that associates or fixes a number to the particular point x. If y=f(x),…

Q: Find R3.3 approximation of the integral. c1 v3

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Q: Find an integrating factor to obtain the integral curve of (2ау — 16х) da + dy 3 0 that pass -…

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Q: •1 r1 Evaluate the double integral / /. cos(y*) Vy³dydx

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Q: Evaluate the integral dx dy by reversing the order of integration.

A: We need evaluate integral using reversing the order of integration∫06∫y23ex2dx dy

Q: Q3/ a) find the integral f 2* * cos2* dx dx b) the integral J e2x+1

A: Explanation of the answer is as follows

Q: (b) Consider the integral I = f f (x)dx for the function f(x) = -2e + 4 1 x' +2x 120 Approximate I…

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Q: Find the forced solution yF (x) at xo Cr³ + c2x³ In(x). 2 to the following ODE in terms of a…

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Q: 6 r5 So f5x dy dx X 1

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Q: 1. Compute the given integral. Using Substitution Method 5x-12 dx = +C 5x2-24x-1 *

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Q: Ex.2. Prove that the complete integral of the equation (xp + yq - 2)² = 1 +p² +q² is (ax + by + cz)…

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Q: i +j- t3/2 k ) dt |

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Q: er Q5:- Find the integral - dx n=8 using Trapezoidal method.

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Q: Solve for F(x) the integral equation F(x) sin xt dt = {2, 1<t<2. [0, t22

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Q: (e² + x² + 2) dæ 1 Calculate the integral with the Trapezoidal method. Take n = 8 (A =x 0.25) for…

A: Trapezoidal Rule : Suppose f(x) be a continuous function on the interval a,b . Now divide the…

Q: Find the Particular integral of the equation (D² + 2DD' + D² )z = e®-y

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Q: dy y(y²+1)

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Q: 2t + 1 What is the indefinite integral of dt ? t3 -8t + 21t – 18

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Q: 15x2-x3-43x - 19 dx Ax + B Jax? + bx + C D The integral can be rewritten as (x +1) (x² – 6x + 13)…

A: First we will find the values of A, B, a, b and c by the method of partial fraction.

Q: 2t + 1 What is the indefinite integral of dt t3 -8t + 21t – 18

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Q: Solve this DE by Separable method  1. (x2+6y2)dx-4xydy=0 ; y(1)=1

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Q: Q5:- Find the integral dx n=8 using Trapezoidal method.

A: Given that: ∫15exxdx   n=8  using Trapezoidal method.

Q: Q2) Solve the following problem over the interval from x = 0 to 1 using a step size of 0.25 where…

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Q: dy dx (xy + 1)2 9.

A: Given- ∫01∫01xxy+12dydx To Find- The value of the above integral. Concept Used- As the above…

Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.