5 6 7 | || ? +y² +²) dx dy e -5 0 0

Q: 3. Evaluate the integral. dx B. + 1 А. 8 2 С. 4 c.- D. - 2 6

A:

Q: С 20 3x-1 хр. -X (3+3 (2) j² dx a Лх lo XS хр sự X Сў-12.d:

A:

Q: O)³ = /1+ (y')² = /1+ (y')* = 3 + d²y dx2 a3y 3? +1 ax3 at

A: Note:  according to our guidelines we can answer only first three subparts To determine the order…

Q: 1 Q2: Evaluate fo y² (x² + y²) dx dy

A: Given :∫01∫01-y2y2x2+y2dxdy

Q: 5. (x* +a')dy= 2x| (x² +a²) +3y dx, where a is constant.

A:

Q: 2 5+4y³ Evaluate f,* S* y dz dx dy

A:

Q: d²y dx²\(1,1) -x? + y? – xy + 1 = 0 ise O A) 3 B) NONE OC) -10 OD) NONE not exist O E) 10

A:

Q: /1- (z² + y²) dz dy dæ ) Evaluate

A:

Q: Evaluate xe-X dx, if it exists. O 1) 1/2 2) 1 3) 1-e 4) It does not exist.

A: We have to evaluate given integral

Q: -1/r' y = e=1/x? dy ax'e-. dr

A: Given: y=e-1/x2 and dydx=axbe-xc Differentiation formula (1) dexdx=ex (2) dxndx=nxn-1 (3)…

Q: 3. (x²)(d²y/dx²)+x(dy/dx)+(2/y³)=0 (hint: set x=e')

A:

Q: e2x -dx =D 1+ex (A e2x + In(1+ e*) + c B 2e2x – In(1+ e*) + C © e2x – In(1 + e*) + C D ex- In(1+ e*)…

A: Integration

Q: 11z Evaluate ſ dz ƒ dz ĵ e² dy.

A: We have to solve the given integration and find out which option is correct.

Q: 3 1-x²-y² e-3(x²+y²+z²)² dz dydx 1-х2 a) Evaluate e-3(x²+y²+z?)² dz dydx

A:

Q: 2 4-x xey – dy dx 4- y b. 0 0

A:

Q: /2 rcos x C T-X 6. [" sin(x + y)dy dz dx n/6 Jo

A: Let, I=∫π6π2∫0cosx∫xπ-xsinx+ydydzdxLet I2=∫xπ-xsinx+ydyPut x+y=udifferentiate dy=duas y=x  then…

Q: (2+ e-#/») d.x +2 (1 -) dy = 0

A:

Q: Non Homo (D4 − 1)y = 0

A: Differential equations

Q: n/3 SS ycos(xy)dydx= - π/ 3

A:

Q: (1) E(x, -x)² =Ex} – nx² | (ii) E(x, –x)(y; -y)=Lx,y, – nxy (üi) E(x, – x)(y, – F) =Ex,(v, - )

A:

Q: 2. Find (x) which satisfies (4e y − 1)dx + e dy = 0. O p(x) = e¯² + 5e-4x O p(x) = 3e e-4x O p(x)…

A:

Q: x+x-2 dx If S (x²–1)(2x-x²) dx can be resolved into A S+ Bƒ f(x)dx + D ƒ g(x)dx , then

A: Using partial fraction to solve the problem.

Q: 2 2 Va? +x + Va? -x² If y = Ja? +x? - Va .2 Show that dy 2a 1+ 2 a? dx 3 Va* – x*

A:

Q: 3 Evaluate: ₁ S 1²,₁ S² [(x²-x²)²] dx dy x+y

A: To evaluate the given double integral.∫-14∫03x2-y22x+y dx dy

Q: 15 S A B (c) D (x+1)dx (x+2)(x-1)² 1 2 -- 9 1 2 " 9 3 -lo 1 9 " - - W|N 2 1 9 3 W|N 3 -S[₂ = A B +…

A:

Q: 2x-x ca ch(y) 3 dy dx = 3 dx dy, then If (A)5, 0 2a+g(1)+2h(0)=

A:

Q: /2-x2 Evaluate *Ty dy dx x²+y² Select one: a. Non of them b. 1 2 - V2 С. 1 1 V2 d. 1 3

A: We will find out the required value of given integral.

Q: 7. If y = e*², then d²y dx2 boins9 (A) (2x)(x² – 1)e*²-2 stod beniu (B) ex2 (C) 2xe*2 (D) (2 +…

A:

Q: 17. If y = x, then dy/dx (a) x²-² (b) x²-1 lnx (c) x²²(1-In² x) (d) x²-²(1–In x) (e) None of these

A:

Q: d²y 1. dx² - dy - 6y = 0, when x = 0, y = 0, and when x = 1, y = e³ dx

A:

Q: x²+3y? 2ху = c (Bali, 2007) dy 0 Ans: In(x + y) + (x+y)² + dx 3x² +y²

A: The given ordinary differential equation is

Q: 8. 12. If y = then what is ? x+4 dx dy = 4x(x + 4) dy C. dx -4Vx + 8 dx dy dy = -4(x + 4) d. dx =…

A:

Q: 3 2 ²²(4-x²) dy dx = 7 0 true O False

A:

Q: y fa(4y) -1.0 -2 1/8 -0.5 -1 1/4 1/2 1/8 0.5 1 1.0 2 Find the E (X), E(Y), V (X), and V (Y). 2.

A:

Q: In3 x B. Evaluate ( [e2x+3y dy dx

A: We have to integrate

Q: 2. [e2y ycos (xy)| dx + 2xe2y [2we?y xcos (xy) + 2y dy = 0 -

A: The solution is given as

Q: 3(1 + P) = 2ty(y³ – 1) dt %3D

A: Let us consider the differential equation dydt+P(x)y=Q(x)yn It is known as Bernoulli's equation…

Q: (Ре?У — х)ӑx — 2е?У (е?у + Рx)dy 2e2y (e2y + Px)dy || -

A: The given equation is P(e2y-x)dx=2e2y(e2y+Px)dx. It is an exact differential equation if ∂M∂y=∂N∂x.…

Q: 3 5. [20 points] Solve (x + y)dx+ dy=0 +x-

A:

Q: dx S is equal to e3x O 1/3 e^(-3x) + c O -1/3 e^(3x) + c O -1/3 e^(-3x) + C O 1/3 e^(3x) + c

A: To find: ∫dx e3x

Q: 4 dx L 11. 1 + (2x + 1)2

A: As per our guidelines we are supposed to answer one question, kindly repost the remaining question…

Q: e -dx = x2 e Find c. 2 If Зе c = In 2 2 c = In(들) In(을) C e르2

A: our objective is to find the c.

Q: -5 #2. Suppose that S„ƒ(x)dx= 6 andS²,g(x)dx= -4. Find S°,[3f(x) – 0.5g(x)]dx.

A: To evaluate the given integral apply the following rules.

Q: •7 49–x² r83–x²-y² x dz dy dx %D 0, -15+x²+y²

A: I am attaching image so that you understand each and every step.

Q: Í (x)dx, iff(x) = Vx -k +1;k-15x <k, k = 1, 2,.n.

A:

Q: 3.3(x² + y²)dx + x(x² + 3y² + 6y)dy = 0 a. x³e2y + 3xy²e²y = C b.x³ey + 3x²y²e = C c.x³e2y + 3xy²e2y…

A:

Q: 9. S(9 + 8y – y²)? dy 10. S (e*–2)² dx e 2x + 4

A:

Q: 7. Find for x2 + y² = y dx 2x а. 1-2у 2x b. 2у-1 с. 1-y d. y-1 e. None of the above

A:

Q: - S (x+1)dx в с х-1 (х-1)?, A If (x+2)(x– 1)² dx , the values of A & C respectively are + %3! x+2

A: The given equation is as follows. Solve the function by partial fractions as follows.