Numerical Integration: 5 (2x² – 3x) dx 2. 2

Q: The orthogonal trajectories of the family of curves y = cx² is A x=ky² B C x²+2y²=k 2x² + y² = k

A: We have to find the

Q: Find the area bounded by : f (x)=e*, g(x)=e* and x=3. A (e³-1)² e3 sq. units B (e³+ 1)² e3 (e²+ 1)²…

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Q: Determine the general parametric solution of the following unsolved differential equations for the…

A: See the details solution in below

Q: Which of the following represents the volume of the solid generated by revolving the region bounded…

A: Given:      fx=x-13       gx=x-1 Volume of solid generated by revolving around the region is…

Q: 2.2 5 (2x² – 3x) dx

A: We have to evaluate

Q: The hyperbolic paraboloid (saddle) f(x, y) = x² - y² + 4 is shown in the 3D model below. Find the…

A: Here, to find the volume f(x,y)=x2-y2+4 between the rectangle R=[-2,4]×[-1,2]

Q: If find the value of a. 3 S₁ S² (x + 2y) dydx = 10, 0 a

A: Given: ∫01∫a3(x+2y)dydx

Q: Transforming S Ⓒ √ 2²-22²2 =2 A -dz 1+z² z²+z B -dz 1- © S с © S D N dx using miscellaneous…

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Q: 1. f (x² + 1)(x² + 3x) dx

A: To evaluate the given integral.∫x2+1x3+3x4dx

Q: 1. Find the area under the curve y = x² from x = 1 to x = 3. -y-x² (1,1) x-1 (3,9) x-3

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Q: z = xey + yex, Find əz əz дх'ду

A: Given: z=xey+yex To find : ∂z∂x,∂z∂y For ∂z∂x, we have to do the partial differentiation of z with…

Q: Using the linearity of the inverse Laplace transform, solve for the solution of the differential…

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Q: Evaluate [C sin(x + y)dxdy. Answer: 0

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Q: The length of a rectangle is given by 4t - 3 and its height is √27, where t is time in seconds and…

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Q: π Evaluate the integral: sin(3x)cos(3x)dx 11/13 B (c) D 1/1/00 H|m

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Q: (a) Verify that tanh P-tanh Q 1-tanh P tanh ọ tanh( P – Q)

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Q: The graph of y=5x*-x³ has a point of inflection at (A) (0, 0) and (4, 256) B (0, 0) and (3, 162) (3,…

A: Given graph,y=5x4-x5Aim : To find point of inflection.

Q: A street light is at the top of a 10 ft tall pole. A woman 5.75 ft tall walks toward the pole with a…

A: Given problem:- A street light is at the top of a 10 ft tall pole. A woman 5.75 ft tall walks toward…

Q: 1 √√√√x + x S Solve the integral: A m/1+x³²|+c C {/in/1+x²³ | +c B © 6in/5+x³³| +C Ⓒ √I/1 .…

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Q: Which of the following can be determined given Ⓒ [² (4f(x) + 9h(x)) dx 3 ® √²³((x) + B © ²(f(x) -…

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Q: A population of bacteria B has a growth rate proportional to B itself. If between 12:00 nn and 2:00…

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Q: 7. Which of the following is the differential equation satisfied by the given by the particular…

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Q: . The Minimum point of y = x3 3x+6

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Q: D sec²u=1+tan²u

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Q: The reverse order of 4 So Say ex² dxdy is equal to e-1 8e None of them

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Q: Q3/ Solve the following. Choose two only. 1. lim x lnx³ X-0 2. lim x sin(1/x) 818 ex+2x 3. lim 818…

A: According to the question, we will calculate the limits of any two subparts.

Q: X √√//dx Solve the integral: A √x 3 B 3√√√x² +C Ⓒ6√√x +C 3√√x² D + C 6

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Q: Question 5 Which of the following is not true? A None of the given choices ℗ √ ² in(x²) dx = I'm √…

A: The objective is to find which option is not true.

Q: HOMOGENOUS LINEAR DIFFERENTIAL EQUATIONS. (D^3 – 2D + 4)y = 0 ; y = –2 , Dy = 8, D^2y = 0, when x =…

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Q: Write TRUE or FALSE before each statement. Solve y + y = ry³. Statement 1. The integrating factor is…

A: This is a problem related to differential equation. Based on the general formula and concept we will…

Q: B/A block of ice in the shape of a right circular cone is melting in such a way that both its height…

A: rate of change of volume of cone

Q: Determine the integral: x²cosxdx A x²sinx+2xcosx + 2 sinx + C B x²sinx-2xcosx-2sinx + C C)…

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Q: In(x+2) 1. S dx 2x+4 2 2. fx² ex dx 3. f tan³x dx 12

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Q: the equation of the tangent line to the curve y = 4 sin x at the point equation of this tangent line…

A: We are asked to find the tangent line of the curve.

Q: Evaluate: dx (x+1) log(x+1)

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Q: Determine the area bounded by the functions f(x) = (x + 1)³ and g(x)= x + 1 3 A 2-unit² 1 Ⓡ / unit²…

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Q: Initially 73 grams of radioactive substance was present. After 3 hours the mass had decreased by 6%.…

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Q: Əz 5. Givenz = y -4x ?х 6. Find of z = In(xy) a²z 7.Find of z= x³ + 5x²y + 6 əxəy Find дz

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Q: To evaluate the integral sin ³0cos (A) sin²0=1-cos²0 1-cos20 B sin ²0 2 sin20 sin cose 2 1+ cos20…

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Q: Determine the 3rd derivative of the given function f(x) = (3x² - 5x + 6)4.

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Q: X lim x→1 x-1 Your answer x In x

A: Let's evaluate given function by using l'hospital's rule.

Q: Solve the integral: S- ® in/1+x A) an 1 B_5n/1+x' 5 6 1 √√√x + x + C + C c dx

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Q: Determine the area bounded by f(x)=x2-x and x-axis. A — -unit² 2 B Ⓒ с D 16 unit² -unit² -unit²

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Q: (D) 1

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Q: 1. ²₂(x² − 2xy² + y²³) dx dy

A: Solve the following integration .

Q: For questions no. 4 and 5. Given: Radium decomposed at a rate proportional to the quality of radium…

A: Using logarithmic function

Q: 17. Find the volume of the solid that results when the region enclosed by y = √x, y = 0, and 2 = 9…

A: According to our guidelines, we can answer only the first problem or first three subparts of a…

Q: Find 4-¹, if A = [3 3 O ] 3 -2 0 O [32] −3 0 - [²2] O −3 12 -=[ 132] -3-2 O 2 3 3 2

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Q: efv. Evaluate dx Use rationalizing substitution. A B 8 √e² - 2 - 2√2 Arctan — √e² - 2 + C e³ − 2 −…

A: Let's evaluate given integral by using rationalizing substitution.

Q: Q3/ Find a volume for the region bounded by 4/X and Y = (X-3)² about the x-axis.

A: