x² + y² – 4 hat fa(x, y) = 2 Va² + y? · V9 - (Vx² + y? – 4) r2 |

Q: xdx 5. I 4x 2 * – 4x +1

A: Given, ∫xdx4x4-4x2+1    ∫dx3x-73 We have to evaluate the integral

Q: Determine  d2y dx2 for y = (4x3 + 8)4.

A:

Q: 3-2 P. (4a² b)x3(ab ³) ==

A:

Q: 7. (D5 – 5D³)y = 24

A: Given problem Given that 7)

Q: xe lF Sx2z+y3-Xリ2う=0,

A: Consider the following equation: 3x2z+y3-xyz3=0 Differentiate the above equation with respect to x…

Q: dx x² Vx² +9

A: Given that a integration of 1/(x2√x2+9). We know that Integration power rule is given  as -…

Q: S Vi+ V2+3xdx

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

Q: Find: d dx (4æ5 За? + 5х — 1) |

A:

Q: Integrate dx Vr® + 4

A: Given integration is                                                              ∫x2x6+4dx here we…

Q: Evaluate: 3 f(-x² + 4x-1)dx 1

A:

Q: /6х — 22

A: We will evaluate the given integral as shown below by using trigonometric substitution

Q: 6. Find (x + 3y)dA where D = {(x, y) | æ² + y 0}

A:

Q: 2 (0² 20 0 Ans v=c₁ +c+.

A:

Q: (x4 4x2 + 6) dx = 2 (x*-4x2 + 6) dx Select one: True False

A: Property of definite integral ∫-pp f(x)dx = 2∫0p f(x) dx , if f(-x) = f(x) or it’s an even function…

Q: y = 2t + t2 – 2(In t)² d.

A: y = 2t + t2 - 2(lnt)2

Q: Determine the antidifferentiation of (3xc + ed - (4/x)) dx  (where c; d are real numbers and c does…

A:

Q: // (3x + 4y)dA where Find D D = {(x, y) | x² + y² 0}

A: Given f(x,y) = 3x+4ydA =dxdyarea bounded by the region x2+y2≤4,x≥0. It is a semicircle in the left…

Q: - dx V4 –x² 14.

A: We have to integrate

Q: dx V 20+8x x2

A:

Q: Зх + 2 dx. 1 – x²

A: Given. We are given a function and we need to do indefinite integration on it. I = INT[…

Q: dx |Vx + 5

A: Explanation: Given that,  ∫xx+5 Let  u=x+5du=12x+5dxdx=2x+5du Now…

Q: Evaluate f(3r2 - V5x + 2)dx.

A:

Q: (t+6)2 dt

A: Given,

Q: / (3x - 3)(3x² - 6x +15)4 dx

A:

Q: d³y of y = (3x*-5)(2x³+9x-6) Determine the %3D dx3 7x5

A:

Q: 9x + 4y = 20 4 2 2 6 x 0 x

A:

Q: y10) f(x, у) %3D In x9

A:

Q: 5 -dx 1+ x2

A:

Q: Vx2 – 4 d.x 3.

A: Please refer the attached image for complete solution.

Q: Find // (4x + 2y)dA where D = {(x, y) | a² + y? 0}

A:

Q: dy 2 y = x3 – 6x3 бх3 — 5; - | dx5

A:

Q: +2

A: To evaluate the given integral.

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.