b) S Ti dx x2+1 V.

Q: Find impicitly, tf e*(eУ — 1) + sin(2x + 5у) %D In(V7) - - сot(2x) y+2

A: Given function is Differentiating with respect to x by using product rule ,we get

Q: If Arctan gx 3. dx =b Arctan* 3x +C, what is b?

A: Solving the given integral by substitution.

Q: a) S xe3*dx = ? to %3D b) s dx ? (x-1)3 8-

A: Hello. Since you have posted multiple questions and not specified which question needs to be solved,…

Q: Which of the following is equal to (2° – 7æ)*dx = (x6 -

A:

Q: -п/8 S sec? (2x)dx

A: We have to evaluate the definite integral: ∫0π8sec22xdx Assuming, t=2x Then definite limit will also…

Q: dy 4. a2+ y? = ry (Bernoulli DE) dx

A: Answer and explanation is given below..

Q: 2. J Зу /7—Зу?dy

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Q: What is the value of I V16 – x² dx?

A: The definite integral ∫-4416-x2dx can be solved by applying the trigonometric substitution . Let…

Q: 19. What is the equivalent value of *Vx+ Tdx 20. In evaluating (&+ Idx x dx which one is to be used?…

A: The solution for the above question is as shown below.

Q: 2 sin(t) s(t) = et

A: Part (a) The displacement of the object is, s(t)=2sintet Integrate the expression with respect to t…

Q: 4-S cosh? Vx dx x csch vx

A:

Q: S'(1 + v=)dz b)

A:

Q: S S, 4cosx² dx dy

A:

Q: b) Sx² sin 3x dx

A: To find :                            ∫x2 sin 3x dx                Let I =…

Q: 2m (b) S* dz. VI+3 sin z cosz

A: Explained below

Q: 2 (4-x² r² dzdydx Q5: Find Si * S,

A: We have,∫02∫04-x2∫x2dzdydx=∫02∫04-x2zx2dydx∫02∫04-x2∫x2dzdydx=∫02∫04-x22-xdydx

Q: 3. Determine the complete solution using MVP: - cot(2:) dx

A: Given the differential equation

Q: 2. I cosh ix dx

A: The given integral is ∫cos14xdx. Evaluate the integral.

Q: If ſ x sin x cos x dx = xsin²x + Ax + B sin 2x + C, what is the value of A + B?

A: The given integral is, ∫xsinxcosxdx=12∫x(2sinxcosx)dx=12∫xsin2xdx=12∫xsin2xdx=12I1

Q: d) S 3x²e*dx e) 2t?Vt3 +1 dt

A: evaluate the integrald)∫3x2exdxe)∫022t2t3+1 dt

Q: If f (5f(x) + 2) dx = 4, then Si f(æ)dx =

A:

Q: Evaluate the integrals

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

Q: rcosA 2. r sin 0 dz dr de

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Q: "4 rseco sin 20 dp do d0 0. 0,

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Q: 2sinh cosh -dx 3cosh? * 2

A:

Q: 7) sinh 2xdx 8) fcosh vdv 9) f cot ydy pai4 sec? Jwdw

A:

Q: tan st dt \+9t?

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

Q: (d) y' + 2 sin 2nx = cosh 3x %3D

A: As per our guideline we are supposed to answer only one asked question.kindly repost other question.…

Q: d sec(11x – 4) dx = dt 13

A:

Q: Eliminate the arbitrary constant ln y = c, sin 3x + c2 cos 3x + 9x^2 -2

A:

Q: to of 3g dx Be

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Q: @ show thatd (csex)=. dx XV x?

A:

Q: When evaluated, | x sinh 3x² dx is equal to A. cosh3x? +C B. cosh3x? +C C. 3 cosh3x? +C D. 6 cosh3x…

A: we will let  3x2= t  to solve this question.

Q: If y= In(3x² – 6x – 8), then find dy. | dx

A: Chain Rule of Differentiation dydx=dydududx................................................(A)…

Q: Evaluate , Sd-2, r2(1-z) dy dx dz

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Q: -CInx) e et XN fex)= ×フ 2下X find E CX)

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Q: c) Evaluate [xV2–x? dx by using substitution method.

A: Integrate by substitutions

Q: 2r – 1 dr = ar" + dx" +C.

A: Integrate the function using basic method. Keep the function in power term. And then compare.

Q: In (x) -dx is equal to x2 The numerical value of

A: Given is an integration and we have to find it's numerical value. Here, we use the Integration by…

Q: Find dy/dz by differentiating implicitly if z2 + y = 100. Answer:

A:

Q: - 7x)4 dx Using an appropriate substitution, evaluate: B

A: The given integral: I=∫x6-7x4 dx

Q: 3 Given that ex dx = e³ – e, use this result to evaluate 7ex + 4 dx.

A:

Q: differen tiatin, de tomine dx リ= (aH) (xs) 5 (as) (x-+)

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

Q: Sx(2x – 3)®dx

A: Solution

Q: 3. to 4. Hox - 9x²+8dx 2- 十一X dx

A: ∫10x4-9x2+8x2dx

Q: dx J Tx2 – 25

A:

Q: If (Mesin(2x) dx = eSin(2x) + C, then the M is equal to-

A: We will differentiate both sides w.r.t 'x'

Q: 19. S.cosTa de cos7x dx 5

A:

Q: If dy/dx = 3x^2 - 3 and y(0) = 8, then y(1) = ?

A: If dy/dx = 3x^2 - 3 and y(0) = 8, then y(1) = ?