2x f(x) = x² - 4 %3D

Q: Find a and b in Va+4x-5 dx = x+2

A:

Q: x2-3x+1 i) S xln²xdx and ii) S7 dx. (x+2)(x2+1)

A: Given: ∫x ln2 (x) dxFormula: (ln (x))'=1x∫ x dx=x22+C

Q: x'e-2x dx 20 dx 2

A:

Q: 2. S (5x-12) dx x³-6x²+8x

A: Given, ∫5x-12x3-6x2+8xdx

Q: (4x3-6х) dx 3. S x*-3x²+2

A: ∫4x3-6xx4-3x2+2dx we know that∫f'(x)f(x)dx = ln|f(x)| +cf'(x) =4x3-6x , f(x)=x4-3x2+2

Q: 1) f3x* dx +x dx 3) fxva² +I dx

A: We know that, ∫ xn dx = [( xn+1 )/( n+1 )] + C

Q: 1. f4x-³ dx -3

A: Find the integral

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

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

Q: 2x - 2x2-3 dx - Find 4 x* + x²

A: To evaluate: ∫2x3−2x2−3x4+x2dx Let, I=∫2x3−2x2−3x4+x2dx ⇒I=∫2x3−2x2−3x2x2+1dx

Q: S (2x² + 1) dx x3 - 3x +2

A: ∫2x2+1x3-3x+2dx This can be written as  ∫2(x2-1)x3-3x+2+3x3-3x+2dx=2∫(x2-1)x3-3x+2dx+3∫1x3-3x+2dx

Q: (x²-2x+11)dx (x²+3x-4) .2. r2.

A:

Q: y(2x³ -x²y + y³)dx – x(2x³ + y3 )dy = 0

A: y2x3-x2y+y3dx-x2x3+y3dy=0

Q: V2/2 -3x2 dx 1 – x²

A:

Q: : س2 : احسب قيمة التكامل x - 2 dx 4x2 + 4x + 1

A:

Q: 3 csc2 V1-4cot² x x dx

A:

Q: 2x2 + 3x – 3 dx X - 9

A:

Q: 2 + 3x + x) dx . 3x² + x) t 3

A:

Q: f3xcos(4-x*)-8xV4=x² dx s(4-x²)-8x/4-x² dx —:

A: Let us solve the integral using substitution method in the next steps.

Q: (x2 - 4x + 4)4/3 dx -

A:

Q: Solve equation for x. e-x = 1

A: Given equation is e-x=1 To solve the equation for x. Solution: Equation is e-x=1. Taking logarithm…

Q: 4. (d) f(x)dx 6.

A:

Q: f(x)dx =| -8 -4 -4 (9f(x) – 7)dx

A: see below the steps and calculation

Q: (2x2-x+6)dx (х2—х-2))

A:

Q: d -(f(x² + 3x)) dx

A: Derivative

Q: (6x-y > -3 13. ly>x-2 14

A: First draw the two straight line 6x-y=-3, y=x-2.

Q: (e) f(x)=(Vx 3

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

Q: 6+ | f(x) dx = 21 and g(x) dx = 14, find (3f (x) + 5g(x)] dx.

A:

Q: 2 S. x*- 4x +4 dx (メ-2)(x4) |

A: Solution: Consider the given integral is: I = ∫x2-4x+4(x-2)(x2+4)dxI = ∫x-22(x-2)(x2+4)dxI =…

Q: glx)=Dx-4 X+9 g(xth)3D/

A:

Q: S (2 + x)dx √4-2x-x²

A: We can solve the integration as below.

Q: 4 dx is equal to: xv16 - x2

A: we have to find the following integral

Q: (x + 5) dx V4 - x2

A: This question can be solved using integration by substitution and using the formula of some special…

Q: (2x³+x-1)dx 1. S x3+x²-4x-4

A:

Q: x3-3 5). S dx V x11

A:

Q: x² + 2x x4 - 3x² - 4 S dx

A: To find the given integral ∫x2+2xx4-3x2-4dx

Q: Sg(x) dx 2. g(x) 3. 3f(x) dx 5. If(x)-g(x)] dx 6. [4f(x)– g(x)] dx

A:

Q: (x3-4) 2. S dx x3+2x2+2x

A: To evalaute: I=∫x3-4x3+2x2+2xdx=∫1-2x2+2x+4x3+2x2+2xdx=∫dx-∫2x2+2x+4x3+2x2+2xdx

Q: + 2r -1 dx (x2 – x – 2)

A: Disclaimer: "Since you have asked multiple questions, we will solve the first question for you. If…

Q: 2x° dx x2-4

A: ∫2x3x2-4dxSubstitute u=x2-4→dudx=2x→dx=12xdu=12∫u+4udu=4∫1udu+∫1du

Q: V4- V4-x dx 11.

A: Solution of question as follows

Q: 2Rx-3 + (x² – 3)] dx а. - (Rx2-3x+1)5

A:

Q: x+1 g). S dx x²-3x+2

A: We have to evaluate the given integral

Q: SV2*- 16 dx 2.x

A: Consider the integral: ∫e2x−16dxApply u…

Q: xª – 5x³ + 6x² 5a3 + 6x2 — 18 dx x³ – 3x2 -

A: The given integral is: ∫x4-5x3+6x2-18x3-3x2dx Let, I=∫x4-5x3+6x2-18x3-3x2dx

Q: x+3 k) S- dx x2+6x-11

A:

Q: e6x (a) : dx 4+ e6x (b) /: dx 4+ e6x 3 (с) dx V4– x2

A: Since you have posted multiple questions i can answer first three as per our company guidelines…

Q: S² 7x2 + 16x – 19 dx x² + 2x – 3

A:

Q: rlog 2 Vex – 1 dx -2 S, x8Vx2 – 1 dx x² x8 dx (a? Loc2)7

A: Sol

Q: X 2 dx = V4-x2

A: I=∫01x24-x2dx =∫01(4-x2)+44-x2dx =∫014-x24-x2dx+∫0144-x2dx =∫014-x2dx+4∫0114-x2dx Here  ⇒∫a2-x2…