The integral of 2xv3 + x?dx by substitution method is 3(3+2²) O 2(312) + C 2(312) + C 3 3(312) 21 2.

Q: Solve the integral: Seln(2x² + 3x-4)³ (4x + 3)dx A eln(2x² + 3x-4)³ (4x+3) 3(2x²+3x-4) (2x²+3x+4)4 B…

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Q: Evaluate the integral (2 + 6) (2? + 6z + 2)*dz by making the substitution u = x² + 6x + 2. + C

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Q: The answer of the integral St v7e + 12 dt is ( + 12)2 + c + 12)/2 +e

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Q: dx = V9x2 + 1 Use the appropriate substitution to evaluate the following integrals: ... /9x² + 1 +C…

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Q: Evaluate the integral dx 2xx - 3x? A -In 4 V2x + V3 +C 1 V3+ 2x B In +C 2/3 V3-2 +C In 2/3 "/7x + /3…

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Q: D. Evaluate the integral: c. A. 2x +C С. + x + C B. 5x + 3x + x+ C 1 D. 3 r'+x+ C

A: Please see the answer in step 2

Q: Evaluate the integral. x dx (7x° + 3)* 5 (7x² + 3) * + c -4 O A. 56 7 O B. -(7x + 3) - +C Oc. -(7…

A: Given query is to find the value of the integral.

Q: The integral of x²Inx with respect to x is; r3 A -(Inx – 3) +C 9 B -(3lnx – 1) + C 3 C ( 3lnx + 1)…

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Q: Find the integral. X. dx 6 6 7 A. -x 7 1 O 2x2 7 OB. – 2x-2 +c .3 Oc. C. - 3x -2 +c

A: The explanation of answer as follows

Q: Evaluate the integral. 3t2 k dt 1 + t2' 1 + t3

A: We have to find integral

Q: Evaluate the integral. 2 4y² – 5y – 12 dy Л Уу + 2)(у — 3)

A: The given definite integral is: I=∫12 4y2-5y-12y(y+2)(y-3) dy

Q: Answer the following. All fractions are in lowest form. 5x² - 3x + 18 dx x(9 – x-) dr 12. r³ (Vr² –…

A: As per our  guidelines we are supposed to answer only first question. kindly repost other parts in…

Q: Evaluate the integral: S (3x-3 + 3)dx Choose the most appropriate answer. ○ 응z + 3z + C O 2x5 + 3x +…

A: ∫xndx=xn+1n+1+C , C is a constant and for any real number n.

Q: 9. Evaluate the integral // V2 + y² + z² – 3 dV where S lies between a² + y² +2² = 1 and a? + y² +…

A: Given integral, ∭sx2+y2+z2-3dV Where S lies between x2+y2+z2=1 and x2+y2+z2=9. The spherical…

Q: a+bx² dx V3ax+bx3

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Q: 2. y(x4-y²)dx + x(x++y²)dy = 0

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Q: Find the integral. |(2x3 - 3x2 + x – 1) dx A x² + B 6x2 - 6x + 1 + C (c) None of the above x2 - x +…

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Q: 2 show that V(x, y) = x 'f (2x+y) is the general Solution of : Xav dx 2x du ду = V

A: We can show given function is a solution of the given equation .

Q: The integraing factor of (4xy+3y² – x)dx + x(x+2y)dy3D0 is (A x-2 B 2x-2 2x-1 D D x2

A: Since, the given differential equation is not exact . To make it exact we find integrating factor ,…

Q: Evaluate the integral S dx 2x3 - 3xx 1 -In 2/2 "I/3x + /2 +C En(2 { x³ - 3x x)+c 1 V2 + V3x -In + C…

A: First we take common x3/4 then put√x=t  And using integration of 1/a2 - x2

Q: Show that the value of Vx + 8 dx lies between 2V2 - 2.8 and 3.

A: According to the question, we have to prove that the value of integral ∫01x+8 dx lies between 2.8…

Q: Evaluate the integral. 20e V5x dx Select one: A. 10 e5x + C B. 45 ev5x + C C. 20 eV5x + C D. 5 e5x…

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Q: Find the integral 17T dx 2+18 1 는시17x + 18+c 17 1 18x - 18 +c b.

A: Solve by substitution integration method

Q: d) Evaluate the integral. 4 – |x – 1|) dx + -12 + 8х — х2 dx + —72 + 18х — х2 dx 2 12

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Q: 2. Solve by using an integrating factor. (a) y' + 2ty = 2te¯ %3D

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Q: Step by step

A: Given integral

Q: Given the integral J6x2 - 4x dx бх2 - 4х

A: Complete the following question involving basic integration techniques. Given the integral…

Q: Q2/Find the value of the integral dx 1+x² by using simpson method (n = 6)? 3

A: Find out the value of the integral using the simpson 1/3 method.

Q: Evaluate the integral : S 8x2+10x-6 (x-1)(x+1)z dx (2—1)(ӕ+1)? +C

A: Given: ∫8x2+10x-6x-1x+12dx To do: Evaluate the given integral.

Q: 16 Evaluate the integral f 2x (x2 + 7)º dx using the substitution u = x? + 7. %3D | 20 (2* + 7)" dz…

A: We need to evaluate the integral ∫2x(x2+7)16dx with the help of substitution. This can be evaluated…

Q: Show that 3x2 +6x +2 = 3 (x+1) - by completing the square. Hence, evaluate the 2 integral dx. V3x? +…

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Q: tan (In |4x²|) dx is bin sec (In |(2x)^)| + C. what is b? The integral of (A 4 1 B c) 2 1 D 2

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Q: Evaluate the integral. 8+e-5x dx e6x 1 44 -5x +6 + C 30 O -8e-l1x(11e6x + 1) + C O .tel1x(88e5x + 6)…

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Q: Solve the eauation In(2x + 2) – In(4) = 2ln(x) O a. x= 0 O b. x= 1 O cx= 2, 1 O d. x= 1, -1/2

A: Given,, The logarithmic equation  ln2x+2 -ln4 = 2lnx  We have to solve the equation.

Q: ar integral of the c 3 – 7D2 + 7D – 2

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Q: Integrate the following: ,S (x4 – 5æ³ + 6) dæ - 1. So(1- r)*dz su(1– 2.

A: These questions are related to indefinite integration, we will use use integration formulas and…

Q: Apply Method of Substitution and evaluate : 6x° 162x dx 8 e 3 e628 6x8 Зе + C, Where C is an…

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Q: Use the IVT to prove thatx^2+ lnx =1/2 has a solution.

A: Use the IVT to prove thatx^2+ lnx =1/2 has a solution.

Q: c4 So So (6x² +9y²) dx dy

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Q: find the integral 4V2 (4 – x³)/² dx 3

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Q: 4. Evaluate the integral. (a) (2r-4r + VE) dz + 4x) dr

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Q: Find the integral. 12x Vx dx 9 24 OA. 7 +C 8 О в. + C 3

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Q: В. .3 x³ In(x) + C 3

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Q: df Use integration to find f(4), if = dx O -26.667 O -19.667 O 26.667 O 30.333 5x2, and f(1) = 7.

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Q: Solve the integral: Seln(2x²+3x-4)³ (4x+3) dx (2x²+3x+4)¹4(4) A + C 3 eln(2x²+3x-4)³ B + C…

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Q: Cx² tq]% /2 2

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Q: Solve the integral: Seln(2x² + 3x − 4)³ (4x + 3)dx eln(2x²+3x-4)³ A (2x²+3x-4) (2x²+3x+4)4 + C 4…

A: A detailed solution is given below.

Q: Evaluate the integral. 1 t3 dt t2 - 4 /2V2

A: ∫2241t3t2-4dt=?

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.