find 45. dx x3/2 – Vx 46. dx 1) Vx (Hint: Let x = uº.) (r'/3 - Vx + 1 47. - dx = dx 48. JxVx + 9 (Hint: Let x + 1 = u².) dx 49. J x(x+ + 1) dx x°(x° + 4) 50. Hint: Multiply by 51. dθ 52. de cos 20 sin 0 cos 0 + sin 20 Vx V1 + Vx dx 53. 54. dx V2 – Vx + Vĩ х

Q: 2x² +1 -dx r'- 3x+2 4.

A:

Q: Calculate dy/dx. No need to expand answer. y=7x^2-9x+17/2x+4 dy/dx=

A:

Q: dx Vx+2

A:

Q: which of the following is equation is an exact DE? a. (x^2 + 1)dx + xydy = 0 b. xdy + (3x- 2у) dx…

A: which of the following equation is exact DE? (i) x2+1dx+xydy=0 (ii) xdy+3x-2ydx=0 (iii) 2xy…

Q: Q Find dY 2. カー×* * (sinx Cosx) Q@ sinx cosX ® (sinx) Ofan Ctanx)

A:

Q: y = sin z

A:

Q: if x^2 + 3y^3 = 12, find dy/dx and evaluate (-2, -3)

A: To find the derivative

Q: d2y Find anž if 2x²-3y²=7 dx2

A: Given that 2x^3-3y^2=7

Q: Ex: Siny dydx

A:

Q: 8x V a8 + 5 dx =.

A:

Q: ysin2xdx-3y°cos?x dy -0

A: The given ODE is: y3sin(2x) dx - 3y2cos2(x) dy=0 This can be evaluated as follows:

Q: To/t Integrate Ua ko To 3. Uz kg 2. eT-1

A:

Q: Find y": Vy - Vx = Va

A:

Q: fostp Ex=(Xzy)=-3:52-25)

A:

Q: Let 5 sin⁡x+ 7 cos⁡ y=6. dy/dx= d^2y/dx^2

A: 5sinx+7cosy=6Differentiate w.r.t x5cosx-7sinydydx=05cosx=7sinydydxdydx=5cosx7siny

Q: Did I do something wrong by distributing the exponent of u^2?

A:

Q: solve 2 (pedoe tydy +2d₂) ² 2 = {(2²-x²=y²2) (seds tydy + z dz/d2} z

A:

Q: | (In x) dx x)²dx 15.

A: Applying integration by parts

Q: dx x'V4 - x² メー 」

A: The given integral is: ∫12dxx24-x2 Substitute x = 2sint, so dx = 2costdt When x = 1, t=π6 When x =…

Q: Evaluate * (1 – x²)3/2° 1 + c 3 1-x2 -1 + c /1 – x² O Option 4 Option 2 2 1 1 + c /1 – x² :+c 3 V1-…

A: ∫ xdx/(1-x2)3/2 here assume that  1-x2 = u -2x = du/dx xdx = -du/2 ∫ -du/2u3/2 ∫ -u-3/2du/2 2u-1/2/2…

Q: dy Differentiate implicitly to find dx exy 2x+9y+3

A:

Q: Consider R4 with coordinates t, x, y, z. Let a = xdt / dx + xdy dz. Calculate a ^ a.

A: Given: is with coordintes .Let .To Find:The value of .Concept Used: