|(181? +t+2) dt dx 8.

Q: Find d'yldx implicitly in terms of x and y. x²y = 4x = 6 dx2

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Q: dx J 2.x² – 3x +9 Зх + 9

A:

Q: (a) By using the substitution, u = 1 + x*, or otherwise, find x3 -dx 1+ x4

A:

Q: Ге-). 5x) dx х Je

A: Consider the upper integral.

Q: Evaluate " " So s L dz dx dy rvZ c3y (8-x²-y² Jx²+3y²

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Q: d | Vsint dt dx 3 2.

A:

Q: ® 2ly*t9) dx +(1-x*)ydy = %3D

A: given DE 2y2+4dx+1-x2ydy = 02y2+4dx = -1-x2ydy2dx1-x2 = -ydyy2+4integrate on both sides to get the…

Q: S: dx V4 + x² (a)by parts, letting dv = dx V4 + x² (b)by substitution, letting u = 4 + x2 3.

A: Integration basically means to find the integrals, i,e. to assign numbers to function in such a way…

Q: 2. (x+53y)e dydx %3D -1J0

A:

Q: 3. fy dy + 10g = e + dt +7 -2t

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Q: dx dy 2 Select one: True False

A:

Q: Show that -a²x² dx = VT/2a, a > 0, I = e by noting that I = -a²(x²+y³), dx dy -a²r², r dr d0. e

A: We need to show thatI=∫0∞e-a2x2dx=π2a,      a>0

Q: d) S 3x²e*dx e) 2t?Vt3 +1 dt

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

Q: 2nsin (пx?) dxdy x2 0,

A:

Q: If fe F dr = Sc(x - 2y³) dx + (x²y) dy, what is F?

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Q: D. Compute in terms of x and y. dx

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Q: x7= - 3x + 18 JZ - 54 in (3+ 57) + c 3/2 2 dx = %3D 3 + VX 3

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Q: dx T 1-x² 4

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Q: 42. (a) By completing the square, show that 1/2 dx T x² – x + 1 3/3

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Q: Q3. Find dt 4x – 2 dx x² + 20 4t

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Q: dM/dt=4M, M=25000 when t=2   dT/dx=-3.2T-1328, T=-212 when x=2

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Q: d sec(11x – 4) dx = dt 13

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Q: dx -3 +2x dt = 2 is

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Q: ( 2x-sy+12) dx +(7x-4y+15)dy = o 2,

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Q: sec2 X dx 3

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Q: find ds/dt. s = t2 - sec t + 5et

A: Given: The function is,

Q: Evaluate

A: Using fundamental theorem of calculus, to find the derivative of definite integral, one need to plug…

Q: 5 (a) | x² In(2x) dx (b) x'e*dx 'xp, Jo

A:

Q: • ["* [*, [° 42²y — 2²³ dz dy dz J1 1. Evaluate

A: NOTE: As per our guidelines, I have solved the first problem. If you want the answers of rest,…

Q: d. Evaluate dx dt (t2 +2t) -1

A: We use the Leibnitz rule of differentiation under integral sign to solve the given problem.

Q: d ef dt (F(=") = %3D dz dz 13

A: We have to find

Q: d V3i dt = dx x²

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Q: T sec"(evE + 1) dx Vxe-Vx

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Q: If ƒ x Inx dx = x² In x – S f(x)dx, what is the value of , 4f (x)dx?

A: Integration is the process of finding the anti-derivative function of the given function.…

Q: 2. Find in terms of Jo and J,: x²½(x)dx

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Q: dx Find So 13 V(1+2x)²

A: Let I=∫013dx1+2x23 find out the integral value of I

Q: e: √₂² ²₁₂₁ (4x²yz - ²) dz dy dx 4

A:

Q: 2r – 1 dr = ar" + dx" +C.

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

Q: d /7+t*dt dx'5

A:

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

A: The given integral: I=∫x6-7x4 dx

Q: |(3nt?t? – t*) (3n² – t') dx - --

A:

Q: Solve Yor メ= o-5 X (6)=0 %3D dy

A:

Q: Find d2y/dx2 for y = tln(t) + 9t, x = tet + 1.

A: Given,        y=tlnt+9t  and  x=tet+1

Q: 4 d 4. Find dx 2 Vt2+17 dt

A: The given integral is,

Q: dx 2. = 3x. dt

A: The given differential equation is                                                    dxdt=3x…

Q: rtan r d Vt3 +4 dt dx 1/a

A:

Q: y=3e2x+3e3x prove that d2y/dx2+5dy/dx+6y=0

A: Given:

Q: 222 d. Evaluate dx Vt²-t dt

A: We have to solve this