а. (4D + 1)(D — : с. (D — х)(D + х)

Q: (3x²+8x-12)dx 1. x3+7x2 + 12x

A: ∫x+1(x-1)x2dxperform the partial decomposition=∫-2x-1x2+2x-1dxApply…

Q: Let (x1, y1) = (7, 2) and (x2, y2) = (1, -1). Find √[(x2 - x1)2 + (y2 -y1)2]. Express the answer in…

A:

Q: 2x+3 a) S; dx x2-3x+2

A: We integrate the following by using substitution rules and factories the denominator.

Q: Find the value of ( x + y ) / (x - y ) if x = 6 and y = - 2.

A: The expression: x+yx-y

Q: Solve (2y +5)dx = 6dy O a. y = 3In(2x+5)+ c O b. x = 3In(2y +5)+c x =- In(2y+5) +c O d. x =…

A: Given that          (2y + 5)dx = 6dy Now we solve this differential equation.

Q: y = (1– 2x) ;y" ¡y"

A:

Q: (- 1)"(品 2n +1

A:

Q: 3 2. x1 + x² dx

A: Definate integration

Q: dx x²Vx? - 4) (x)

A: By substitution method, solve the integration. Put x = 2sec(theta)

Q: (7x+19)° 57°

A: sum of the angle of the triangle is 180°

Q: Integrate dx Vr® + 4

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

Q: Q2:- xdy-ydx -Jx - dx

A:

Q: (x + 4) dx (x + 2) Vx +. 5

A: To evaluate the integral: ∫x+4(x+2)x+5dx Direct integration is not possible, so we will use the…

Q: x2 dx - 1

A: See the details solution in below

Q: dx -2 3 (5-4x- х?)2

A: Let's find.

Q: Find curl (5z i + 6x j + 2y k). curl (5z i + 6x j+ 2y k) = ( i )i + ( i )j + ( i )k Save for Later

A:

Q: 2 с. dx

A: topic - definite integration

Q: (3 2X +2X +2 dx x²+2x=x -2

A: As per guideline we have to solve

Q: (2x2-x+6)dx (х2—х-2))

A:

Q: 13x+30= (류,-1) and (-3,) 4. Find the equation that contains 7'3)

A:

Q: дz дz 45. Find and Әх ду at (-1, 1, -1): yey-x² +z² = -3z-y²³

A:

Q: x3 dx 10. x2 + 2)

A: As we know that the Power Rule: ∫xndx=xn+1n+1+C ; n≠-1 And ∫1ax+bdx=1alnax+b+b From the given…

Q: (x2-3) Cx²+ 2) S dx J3xx3

A:

Q: a) [(5x4 + 3x² + 2x + 4)dx b) [(Vx² + 7x)dx

A:

Q: Draw a picture of Cay({2, 5}:Z8).

A: Given,            Cay2, 5 : Z8.

Q: ∫t4(t5−2)3dt

A: We have to solve

Q:

A: Given,       x-x=

Q: ky5 | 7 (x³V5+ 8)(5k² - - x2 dx

A:

Q: (2x³+x-1)dx 1. S x3+x²-4x-4

A:

Q: = (2xy + z² )i + (x² +z)j + (y + 2xz)k, determine a possible value for .

A:

Q: y=arctan(5)- 72x2 + 49)

A: The function is given by,

Q: Solve for ‘x’ and ‘y’:(a – b) x + (a + b) y = a2 – b2 – 2ab(a + b) (x + y) = a2 + b2

A: Given,

Q: (15x - 8) 226

A: Given,

Q: 3 (2x2+3x-1) dx х3+5х2+6х 3.

A: ∫2x2+3x-1x3+5x2+6xdx Lets factor the denominator part x3+5x2+6xxx2+5x+6xx+2x+3 ∫2x2+3x-1xx+2x+3dx…

Q: x-2)3+(y1)3

A: Given: x-23+y13 To simplify the given expression:

Q: dy 2 y = x3 – 6x3 бх3 — 5; - | dx5

A:

Q: Divide 8r*y – 10x*y³ + 12x²y³ by 4.r°y?.

A:

Q: La (x3 – 2x)dx -2

A:

Q: +2

A: To evaluate the given integral.

Q: x = (1- y)*(3y +1) ;y"

A: Answer is given in next step.