3. 1. Sdx 2. Sa+2 2x+1 dx x+1 3. S: dx x²+2x+5 1 4. Sdt 5. S dt 7t-1 (4-1 dt S 5-t3 6.

Q: ind dy/dx. y= -3x square root of 1-4x^2

A: Differentiation of the function with respect to x helps to find the derivative of the function.…

Q: 1. S 2. [x²e²² dx 3. [sec* (x) dx 4. fxinx dx 5 ( x50x² dv x arccos x dx 6. Jese² (3x) dx 7. fx³ež…

A: Since multiple questions are asked, I am answering first question

Q: 5. 6. Sexcos2x dx |— S- dx 3 (x + 2)² − (x+2) ² -

A:

Q: Compute dy / dx and d2y / dx2              x 2 - 4y 2 = 8

A: The differentiation is a process of finding the rate of change of one variable with respect to…

Q: 1) dt2 +k²x = 0 2) ax² 3) (x² + y²)dx + 2xydy = 0

A: "Since we are entitled to answer up to 3 sub-parts, we will answer the first three  as you have not…

Q: dy If y = (5x + 1)(2x +In x), then will be %3D dx (5x + 1) +) + 5(2x+ In x) A. -1 B. (5x+ 1) - 2. +…

A: The given problem is to find the derivative of given function y=(5x+1)(2x-1+ln(x)) , we can use…

Q: 7.5- yy - 9 4+9) dy -6- 8.S 1 dx e2x+ e-2x

A:

Q: 2 4 Evaluate Sx dz dy dx 3

A:

Q: 15. /7.- dt 16. x+ 3 dx P + f - 21 2r - &r

A: Solution:Given      ∫dtt3+t2-2tFormula:∫dxx=log x+C

Q: 4. 5. (3t dt)/((t² + 3)) dx/ (3x + 1)

A: You have asked multiple questions and not mentioned which question answer you need so according to…

Q: 1. S 3x° + 2x3+7x - 4 dx 2. Sx7 – 48z11 3. S 10t-3 + 12t-9 + 4t³ dt 5z16dz -

A:

Q: Example 3: Estimate S, x² dx with n=4 by Midpoint Method. Solution:

A: Here first we will divide the integral range into 4 equal parts and then we will calculate the…

Q: 2x+2 dx. 5. x2-2x+1 dy 6. 5. if y = (1+ x²)etan-1x

A:

Q: 4) Find the singular points, residual values, ond of +he = (2 function,

A: The given function is f(z)=1(z2+2z+2)3 The singular points are the points where the denominator of…

Q: 5. ft² √1-1³ dt 6. J (2x+3) dx (x²+3x-6)⁹

A: Given 5. ∫t21-t33dt6. ∫2x+3dxx2+3x-69

Q: If y = u² + 6u - 2 and u = 4x² + 8x + 1. Find dy/dx.

A:

Q: 8. 5x* + -- * ) dx +2 (x³ + In x – e*) dy = 0; y (1) = 0 %3D

A: Differential equation solved by using integrating factor

Q: 1. (2x – 3y) dx + (2y – 3x) dy = 0 - -

A: According to our guidelines we can answer only three subparts of a question, or first question and…

Q: 4. If Kx)dx = k, ] fx)dx = (x-f(x) )dx what is the value of Ax)dx? Use: [Ax) - g(x) ]dx =[ fx)dx-J…

A:

Q: Find dy/dx.  X4y1/3 + e7x - y = (x3 - 11)6

A: X4y1/3 + e7x - y = (x3 - 11)6  dy/dx = ?

Q: Find d^2y/dx^2 at (-1,-2) if 3x^3-2x^2+x = y^3+2y^2 +3y.

A: Given function is: 3x3-2x2+x=y3+2y2+3y Let us consider: y'=dydx ; y''=d2ydx2 Differentiating both…

Q: 7. Integrate em***)dx_using the Substitution method. x +3

A: To evaluate the given integral using substitution method.

Q: 2 Evaluate S S dx dy dz.

A: Evaluating the definite integral

Q: L{t – e-3t} = + s-3 L{t – e-3t} = =-- I. II. s-3 L{t – e-3t} = +3 L{t – e-3t} = III. IV. %3D s+3

A: We know the Laplace transforms Ltn=n!sn+1, s>0 L ea t =1s-a, s>a Now, Lt-e-3t=Lt-Le-3t L t…

Q: (2,5, – 6) | 16x dx + 4y dy + 2z dz (0,0,0)

A:

Q: 4х Compute dx Vx2+1

A: Given,           ∫354xx2+1dx

Q: 7. [(4cosx+3sin.x)*dx 8. ſcos°(3y)dy 1 (у-5)3 v – 5)³ 9. -dy 7 y3 (3 – 2 cscx)² 10. cotx

A: Integrate above function.

Q: 4. Compute (a)음(3e2-4) dx (b) 4 dt dx-x 1+t2

A:

Q: 1. So² – 1),/ỹdy ²+1 2. S dx +3x 3. SEVT + 12 dt 4. dy 5. S 4-3 6. J +5x*+16+1

A: topic - indefinite integral note : as per bartleby guidelines, we are supposed to answer only first…

Q: (x + 1)2 + y = Inx; y(1) = 4 dx Oyx + 1) = xlnx – x + 9 Oyx + 1) = xlnx – x + 8 Oyx + 1) = xlnx – x…

A:

Q: .3 +3 dt dx X

A:

Q: Inx+1 dy will be dx If y = then 2x3 – 3x' (2x³ – 3x) +1) –- (In x + 1)(6x? – 3) А. (2x³ – 3x)² (2x3…

A: Using derivative rule of (u/v),

Q: Find the first and second derivative. S=4t^3-3t^4 Ds/dt= D^2s/dt^2

A: Explanation and solutions is given below....

Q: find dy/dx: (x+y)3+ (x-y)3=x4+y4 ?

A: The given equation is x+y3+x-y3=x4+y4. Find the derivative dydx using implicit differentiation as…

Q: 1. S(x +5)5 dx 2. S(9+ x)² dx 3. S(2x +5)3 dx 4. S(3x + 5)²dx 5. S 2x V1 +x² dx 6. Sex+3 dx 7. S5e3x…

A:

Q: (х — 4у — 3)dx — (х — бу —5)dy — 0 -

A:

Q: ,1 .-2x +5 Evaluate | 3x 10-4x - 2y dy dx 25 3 25 26 7 27 5 28 3

A:

Q: 3 [[ 3x² + 4y dy dx = [[ 3x² + 4y' dx dy 4y³ We have Select one: True False

A:

Q: x2 -dx 1+ x4 -dx (x² + 1)²(x² + 2.x + 2) 1 -dt, for a> |6|. > [b]. а a +bsent

A:

Q: 3x Question 4 Evaluate dx. 4 + e6x 3 Question 5 Evaluate dx. V4 – x2 | 3x Question 6 Evaluate dx. V4…

A:

Q: 1- [(2x – 5)/3x – 1) dx | 2- S S(x3 – 10 + 3y² dy dx

A:

Q: (3x² + 8x – 12)dx - x3 + 7x² + 12x x² – 12x + 4 dx (x2 — Зх + 2)2 t² + 4t + 10 dt t3 + 2t² + 5t dy 3…

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

Q: Find dy/dx of 10x - 18xy2+10y3 = 48 9y-20x 3 (бу? -5ху) dy !! dx 9y-20x dy 3 (буз - 5ху) %3D dx dy…

A: topic - implicit differentiation

Q: 2 - S tần² (3x)sec²(3x)dx

A:

Q: 1- dt 2x 1 d Q10:- Calculate dt dx 2x 3- dx 'x SLn(t) dt. dx 'x

A:

Q: 3x 6 1 -In xy dx e-In √x dx +dy +=dx = e-mxx y X

A:

Q: -1 x-x2 dx -8 2도 1423 1521 22 20 Option 1 Option 2 1425 1523 22 20 OOption 3 Option 4 None of the…

A: Given problem:-

Q: 4. (6xy³ + 2y*)dx + (9x?y² + 8xy³)dy = 0 5. (у2 — 2ху + 6х) dх — (x? — 2ху + 2) dy — 0 When: x =…

A:

Q: 1. S Vx²-1 dx dx 4. S x² /x2-9 dx 5. J 16-9x 2. S dx x/16-9x2 4-x2 3. J 1+x2 dx

A: Given