1 -dx = A(BIn|2 + x|+ Dln|2 – x|) + C, then the value of 2A(B – D) is If 4– x2 O-1 O 2 01

Q: by first- shifting find L(t2 e-3«) = %3D (s+3): ; * 0 a O (s+3) 2 * b O 3.cO (s+3) 3 1

A: Solution:- Correct option :- a Detailed explanation

Q: 5. Use Green's theorem to evaluate where C is shown below (6y - 9x) dy — (xy - x³)dx (-1,4) (-1,-1)…

A:

Q: S(2- sec2x) elmale sec³x sec(3A – x) e ln (xle) What should be the value of A for dr to be…

A:

Q: 32. Find the integral: dx k² +1 (-1)*2 (k² +1) а. +C 5(-1)*2*k k? +1 k+1 b. +C (-1)*2* '(k +1)(k²…

A:

Q: Q6) Compute the integral 3 1 dxp -з (х +2)3

A: Here we solve the given integral.

Q: 13. Consider the integral | - dx then (which statement(s) is/are correct): x2 - 4x (i) dx : x - 4x…

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Q: f A is a 2 x 2 with det(A) = 5, then det(4A-1) = %3D 80 -) 20 16 5

A: We have to choose the correct answer from the options according to the given condition

Q: 3. Evaluate the integral. (a) -2/3 dx

A: Evaluate the integral

Q: 3. [20 points] Calculate the integrals: (a) (b) |(2+ 4)(2r – 1)dz (c) (d)

A:

Q: .(1) t is straightforward to show that y = k-1 is a solution to the homog quation

A: Given,                yk+2 -2k+1kyk+1+ kk-1yk=0         (3.151)and       yk+2 -2k+1kyk+1+…

Q: x2n+1 El-1)"; 2n +1 n=0

A:

Q: Expand x?y + 3y – 2 in powers of x + 1 and y – 2. (up to third degree terms).

A: Given :- The given expansion x2y + 3y-2 in powers of x+1 and y-2.

Q: Q2. (a) Show that {e-*,xe-*} is a fundamental set of solutions of y" + 2y' + y = 0 on (0, 0). (b)…

A: Introduction: Wronskian of a given set of functions is very useful to examine whether the functions…

Q: The ODE d'y -3y = 0 is a Cauchy-Euler equation and has one solution of the %3D form y =r for some…

A: Cauchy-Euler Equation: The differential equation…

Q: (a) Evaluate the integral 9x"e¬X dx for n = 0, 1, 2, and 3. n = 0 9. o((-") - (-1)) n = 1 е | n = 2…

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Q: Evaluate the integral S dx 2x3 - 3xx 1 -In 2/2 "I/3x + /2 +C En(2 { x³ - 3x x)+c 1 V2 + V3x -In + C…

A: First we take common x3/4 then put√x=t  And using integration of 1/a2 - x2

Q: Let f(x, y,2) = x² sin y+y e", where x =t +3,y = ne*-1 and z = In 2t. at t = 1 is: -2 1+2n O -12n…

A:

Q: prove that F(r) = 4z-3z is chaotic on the interval [-1,1]. (Hint: consider g(6) = 30 on S'.)

A: The given function: F(x)=4x3-3x The given interval is [-1,1] To prove that F(x) is chaotic: Chaotic…

Q: What is the Wronskian for y" + 3y = In x? & W 3 b. W = 3 c. W = V3cos 3x-V3 sin V3x d. W 3 cos 3x -3…

A: Here, the characteristic equation is m2+3=0. So,                         m2+3=0⇒m=±3 Thus, the…

Q: Evaluate the integral. 36-² 1 [²+² -√36−x² (x² + y²)¹/2 dy dx dz

A:

Q: Evaluate the integral. S. 3n/4 -8 csc 2 x dx T/4 Select one: A. 16 В. 8 C. 0 D. -16

A:

Q: Find the general solution of ху — у 3D 2x In(х). а) Оу%3D х In(x) + Сх b) Oy = x(In(x))² + Cx с) Оу…

A:

Q: 5. (a) Find the real constants P, Q, R, for which 3 P Qx + R x2 – x + 1° x3 + 1 x + 1 | Show that V3…

A: 5(a)  3 / (x3+1) = P/(x+1) + (Qx+R)/(x2-x+1) ......(1) Now, 3/ (x+1)(x2-x+1) = P/(x+1) +…

Q: 10. Find the integral of dx x²-4 O In() + C x-2 O In() + C 2x x+2 O fIn( *2) + C X+2 O In() + C x+2…

A: *using concept:- 1. Partial fraction. 2. int(dx/x) = ln(x). 3. ln(m) - ln(n) = ln(m/n).

Q: 00 2dx %3D x2 - 1 3. A. In3 B. In2 C. In 3. 3. In - D. E. In-

A: ∫3∞2x2-1dx

Q: 7. Evaluate the integral r8-2x (x + y + 1)-2 dydr.

A:

Q: 0 0 и(0,t) 3D 0; и(1,t) 3D 0; t>0 и(х,0) 3D 5seппх ди a2u = 2 at 1 E sen3пx; 0 <x<1 - 5

A: Given ∂u∂t=2∂2u∂x2  0&lt;x&lt;1 ;t&gt;0u0,t=0; u1,t=0; t&gt;0ux,0=5secπx-15sec3πx ; 0&lt;x&lt;1

Q: If y is a solution of y(x)-[(x-1t)»(?)dt = 1, then which of the following is true? (a) y is bounded…

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Q: ar integral of the c 3 – 7D2 + 7D – 2

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Q: Consider z1 = 1- j2 and z2 = -2 + j3. What is the result of 5z1 + 3z2? %3D -1 -j O 1-j none of the…

A:

Q: B. Switch the order of integration: cos (x2) dædy. Just SET UP with the order switched. DO NOT…

A:

Q: 1 if Pn (x) dx32 . then n= -1 0.a o none of theseco -1do

A:

Q: 8(z+6) Evaluate the integral J -16) dz over C: z - 2+3i| = 4. 1-i O 1+i 3 3i O None of the above…

A:

Q: dx Evaluate the integral: (+3x-7) A ++ In|3x-6|+C 5 +5x+! In/x-21 +C B 3 с +5x+31n|x-2|+C D x² + 5x…

A: You must have idea about logarithmic properties to simplify this expression. Understanding of…

Q: z'e? dz

A:

Q: Exercises 1-3. Evaluate for 2:0s xS1,0sys3. de dy. e*** de dy. 1.

A: As per our guidelines, we are allowed to answer only one question. Since, you have posted multiple…

Q: 21. The equation x - 2·* - 0 has a root in the interval A OS x s1 B ISXS 2 € -1s x < 0 D -2 < x s-1

A: Exponential equation

Q: 1 3 3. Use the IVT to prove that y = x ln x has at least one zero on 2' 2

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Q: 3. Prove that So 0 1 x + ex -dx = n=1 (−1)n−1(n − 1)! nn

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Q: 32 1 xy+- |dydx Evaluate: 2 1

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Q: 5. Let a > 0, find the "generalized solution" to a" + 3x' + 2x = 8(t – a) with x(0) = 1 and æ'(0) =…

A:

Q: 1.Find a general solution of each O.D.Es. A) y" 19y = coqx +os 3 - šin 2 (3) y" + 4y/ + 6.25у —…

A: First we determine the general solution of the related homogeneous equation.  auxiliary…

Q: Evaluate the integral. 1 8 dt V15-21-? - 1 OA. 6 В. O C. 4 D. 3" O D. co fm

A:

Q: Evaluate the integral. 2 [ 11t sec-'t dt 2/√√3 2 S 11t sect dt = [ 2/√√3 (Type an exact answer,…

A:

Q: In x + In(x – 1) = 10 In(x + 25) – In(x – 1) = 3 e2x – 2ex = 15 e2x – ex – 12 = Q %3D %3D -

A: i) ln x+ln(x-1)=10ii) ln(x+25)-ln(x-1)=3iii) e2x-2ex=15 Note:      Multiple part question are given,…

Q: dx Evaluate the integral: 3/2 64 -

A: To solve the given integral problem.