Question 1 V2 + x°dx dy V

Q: Question 5 A | (x – 1) VE dx = AVE - +C B) zi + ei +C c)능z2 - z+C D E) 글교2+2x-a +C

A:

Q: Question 4 dx Evaluate Vä(49+x) Vx 2 Arctan 7. + C 7 Vx 7 Arctan + C Arctan 7. + C 7 Vx Arctan

A: To solve the following integral

Q: 41. e* sin y d A, R = [0, 2] × [0, 4]

A:

Q: 2. x²y² = 3y' +1 dy %3D dx

A: Please refer the attached image for complete solution.

Q: dy IN QUESTIONS 1-13, FIND dx' 1. y = (2x³ – 9x + 1)°

A:

Q: Question 6 a) Given that y = 2x – x? + 3 i) dy Find dx d?y Find dx? ii) iii) Hence, solve the…

A:

Q: QUESTION 2 ay% = 4y³ + 7x dy Find dx

A:

Q: dy IN QUESTIONS 1-13, FIND dx' 8. y = tan8x

A: The solution is given below.

Q: QUESTION 4 If y = (sinx), show that %3D (1 – 2) dy dy 2. dr? dr

A: Explanation of the answer is as follows

Q: Question 25 The general solution of (D2 -2D+1)y=2sin x A y=ce*+c2xe*+ sinx B y=cqe*+c2xe* +2sinx y=…

A:

Q: Question 2 Test the exactness of the following equation then solve the equation: (y In y) dx + (x –…

A:

Q: Question 7 (a) Find if x² + y² +xy=1 dy dx (b) Identify the nature of the stationary points of y =…

A:

Q: Question 19 d'y If y = x In x, find dx2 A) -1/x B -1/x2 1/x2 D 1/x

A: Product Rule of differentiation : d(u.v)dx =u.dvdx+dudx.v d(xn)dx=nxn-1 d(lnx)dx = 1x

Q: QUESTION 1 1. Which of the following equations is separable? (a) y = e*v ez-vy? + e*+vy = y (b) dy…

A: To find  Which of the given equations are separable

Q: dy IN QUESTIONS 1-13, FIND dx' 11. y = x®tan³x 12. y = Vcot3x 15. y = cot"(4x + 9)

A: Find dydx for the following (11) y=x8tan3x (12) y=cot3x (15) y=cot74x+9

Q: 1) S , (x + y) dx dy

A:

Q: Question 4 Solve y at x = pi/3. cotx dy/dx = 1 - 2y, y(pi/4) = 1 0.75

A:

Q: QUESTION 1 dy Find the general solution (x+ 4)- +3xy=x y(0)=1

A:

Q: Question 7 dy Find dr where y is defined implicitly by the equation a4- 5a y7 8 |3D dr 5y7 10y 422…

A:

Q: 1- L,y² e*»dydx

A: In the given integration , order of integration is dydx which imply first integrate the integrand…

Q: Question 6 Find the solution. (x+e')dy– dx =0 A y=ce' + xe" B x=ce' + ye' © y=ce*+ye' D x=ce" + ye"

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

Q: Question No.07: f Y=xi+ i work aut V. ) y9+gk and y = |Y),

A:

Q: QUESTION 12 Find d²y/dx². x=1+1²y=t-³

A: Given;  x=1+t2, y=t-t3

Q: Question 2 Test the exactness of the following equation then solve the equation: y In(y) dx + (x –…

A:

Q: 0. ° (x? + x) dx -2

A:

Q: Question:5 Differentiate with respect to x y = x* e* sinx Inx + xª

A: The given term is  y = xx ex sinx lnx + xe^x.

Q: dy IN QUESTIONS 1-13, FIND dx' 3. у %3DV11 — бх

A: Given that       y = √(11-6x) We have to find dy/dx .

Q: Dind da 2 uit

A:

Q: Question 24 2ay" =17 when t=V2. y' If x= Arctant3, y=/1+16, find the value of a if A 2/2 - 2/2 В ©…

A:

Q: Question 14 Solve the following DE: (2xy? + 3x?) dx + (2x²y+ 4y) dy = 0 O a²y? + 3x + 4y = C O a'y?…

A: Solution of differential equations

Q: Question 7 Given : A B E 0 2π 3 F|+ π 4 (U) =|m x³sin(2x) dx = 3 5π 6 3πt 4 277²-24 64 Find bif sbst

A:

Q: dy IN QUESTIONS 1-13, FIND dx 9. y = 3sin®x

A: Solve for derivative

Q: Question 3 : 2y!ly y" +2)=xy'k

A: As per the question we have the following first order exact differential equation : 2y'(y11 + 2) =…

Q: Question 2 when x 0 and y=3 Compute dx A) 18y B) 18+6y" 6y D) 24

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: Ev 2 x 2 [x²z dx - yx² dy + 2 dz along the curve C'shown in the figure. AZ 2

A:

Q: e) s = cos (1– 21) -2 4t f) y = t+1, .2 x + x g) y =

A:

Q: QUESTION 1 d²y Find dx² for each of the following equations. a) y = 3x² + cos(3x) b) y = e** + (x +…

A: Given that: (a)y=3x2+cos(3x)(b)y=e4x+(x+1)4

Q: Question 11 dy =cos (x+y) , use the substitutions dx To solve the DE A z=cos(x+ y); dz= - sin(x +…

A:

Q: Problem 19  Assuming B=/ 0, compute ∫((Asqrt((x^2)-(B^2))/x)dx in terms of A and B.…

A: To evaluate:

Q: Question 3. Integrate the following: V1 – xª dx

A:

Q: QUESTION 14 Find d²y/dx². x = t + sint, y = t - cost

A:

Q: Question # 4.7 43 Find the valve of (I+J3 243

A:

Q: IVICCE dy Find from the following equations dx Problem (iii) x³ + xy = 0

A:

Q: dydx COS (4) LL dydx + y? x² Vx4

A: Given Double Integrals are: (2) ∫01∫0xcos12πx2dydx (4) ∫01∫x21x3x4+y2dydx Her we use the integral…

Q: Question 20 Evaluate: o So So (x+y+2) dz dy da

A: In this question we have to solve triple Integral.

Q: dy A. dx ay = xy', y(0)=1

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: Question 8 dy The appropriate substitution to solve dx + In(x + 1) = x°y³ is %3D O y = vx O z = y? O…

A:

Q: Question 23 Find the integral. [(3x2 - 4x + 7)dx A) бх — 4 + C (B 2x3 – 2x² + 7x + C x2 + 7x + C C 3…

A: Given

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.