b) 24 dy yVy-16 c) x + 3 dx 2x - 8x

Q: Consider ,- (x3+y²). Evaluate dx² O (9x4+6x)e «³+y?) O (6r²+ 3x)e (x³+y?) O (6x4+9x)e (x³+y?) O…

A: The formulas used in the solution are as follows: 1. Chain rule: df(t)dx=dfdt·dtdx 2. Product rule:…

Q: (2у? + 4л?) da — rуdy — 0 - %3D

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Q: Evaluate ff, x² In(y + 1) dA where R = [0,1] x [0,1].

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Q: sketch > reverse , the then evaluate inlegration 2X (4 x+ 2) dydx X 2

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Q: find? dz =? %3D X = In(4 Cosu) y=4Sinu

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Q: Show that (a) 8(at) =8(t), (b) 6(t) = 8(-t), %3D %3D la|

A: Consider the provided question, Hello. Since your question has multiple parts, we will solve first…

Q: 7 .TT/2 *3 [¹²³r r cose dr de dz

A: Given: I=∫-17∫0π2∫03rcosθdrdθdz   We know that; The Power Rule: ∫xndx=xn+1n+1+C The common integral:…

Q: хр %3D хр if y = In(7x2 + 6y?). Ap %3D Find seng OM

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Q: 1.y" — у' — 2у 3D 7sinh3t — Зcosh3t ; У (0) 3 2, y'(0) = 4

A: The given differential equation is y''-y'-2y=7sinh3t-3cosh3t; y0=2, y'0=4. Calculate the values ys…

Q: 2y+8 2xe to %3D y10)=8= , yco= 2

A: I have solved by using formulas and series expansions.

Q: seclyltun Cy) -csc?(y!dy

A: Use formulas of integration to evaluate the given.

Q: Find ƒx (x, y)  and ƒy( x, y) .

A: Differentiate the function f(x,y)=ln|2x2+y2| with respect to x and keeping y as constant and carry…

Q: 2.) ² - 1) 1 dy (у? —

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Q: Evaluate ze -dz, where C is z+ 2 ((+2+2)?

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Q: ctions. Then give the horizontal asyr 4x 37. f(x) = 20x + 1

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Q: ax 5x +16

A: Our Aim is to integrate:-∫dx5x2+16-(i)

Q: Find mZB. C 10 10 D mZB %3D Submit

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Q: 18. 9y" – 6y' + y = 0, y(0) = 3, y'(0) = 1 %3D

A: Note:- As per our guidelines, we can answer the first part of this problem as exactly one is not…

Q: Evaluate using the tabular method s 5x*ex dx

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Q: ху? + х — 2у + 3)ӑx + x?ydy %3 2(х + у)dy, when x %3D1, y %3D 1

A: Answer and explanation is given below

Q: sec? (1/x) dx. 9: (16pts) Evaluate

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Q: 3 sin y prcos y 2. xdzdxdy

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Q: Se xye" dy, C. x- , y-, z- , 0 <te1

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Q: У(2x? — ху + у?)dх — x? (2х — у)dy %3D0;B у(1) - H IN

A: Use homogeneous equation

Q: 4 Evaluate: ₁₂ (4x²y – z³) dz dy dx

A: We can evaluate the integral  ∫13∫-24∫10(4x2y-z3)dzdydx.

Q: SU = 94 in ; OU = (9x – 16) in %D %3D

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Q: a) fx² sec2

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Q: 5) Зхуdy %3D ху?dy — ydx + 3dx

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Q: 2. If mPA - 36, find mРВ: %3D %3D • C B

A: Solution:Given m PA⇀=36To find m PB:⇀

Q: )find dy to yalog,o(3X+1)

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Q: 1. b. X %3D in

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Q: Calculate || xVy² + x²dA, Where R = {(x, y) /0 < y <land 0 < x < y}

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Q: 6. dyda ydyda 2R Sys of 37 15D to

A: Formula Used:-(1) ∫a2-x2=xa2-x22+a22sin-1(xa)+c(2) ∫xa2-x2 dx=-(a2-x2) 323Consider,A=∫02R∫0R2-(x-R)2…

Q: 1 If Y = x? dy = ? then dz · +c O 22? O 2x 2 dy If y = 6x + 2.5x² + 7x + 2 then dr

A: 1. Given y = x2 So dydx = ddx(x2) = 2x Answer: 2x

Q: Differentiate y = (t^2+2)/(t^4-4t^2+5)

A: We have to find differentiation

Q: d. {(x, y)| y = 3x – 8} {cx, y)ly = } x+3 е. %3D x-5

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Q: - 11. х? %3D 8у - 13. у2 3D — 24х 15. у%3D y 3D — x?

A: As per our guideliness, we are supposed to solve only three questions.Please repost the remaining…

Q: tind y 3 O y=(++ y =9tan 4 ® y= x (2x+1) (4) %3D 1-VX

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Q: $ Find the goneral Solutim of the differen tial equatim : (D²-60 +10)y =20-e2x

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Q: #8

A: We are going to use the formulas:

Q: a.y=(x6+1)2o %3D

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Q: -3D 3I5

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

A: Integrate by substitutions

Q: 37 Го fо7 (xsin(у) — усos(x) dxdy %3D 2 2

A: ∫02π/2∫03π/2(xsiny - ycosx)dxdy in this this is double integration so in first we take y as constant…

Q: UH = 19 FH = 5x-7 H. E %3D U

A: Given - A parallelogram(figure) To find - Value of x in the given figure

Q: x". 2x*+ 3 ×

A: Given, y=x10-2 x9+3 x8

Q: 2x+3y 1. Find the perimeter of the trapezium in Figure 5.91 2x+y x+y+9 if x =9 and y = 7. 3x-y

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Q: dy 16x 9. If r? + y² = 8 then show that dr?

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Q: 5: Derive the formula for trapezoidal Rule to evaluate ff(x) dx

A: