Find the Area of the hegion baudded by the ghaphs Of y=x3 and Y = 4x Using integtation Determine the area by integrating oven the X axis or Y axis whicheveh seems Anche convenient Area Cf Regian A =

Q: x = 2y X=y-8 -12 12 -8-

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Q: 20 Q41. Term independent of x in expansion of is? бх3

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Q: R={ (x,y): 0<x, 0<y, x² +y? <9} be enclosed region. The result of the following double integral (by…

A: We have to find value of given double integral.

Q: S sin®xdx

A: ∫sin6x dx       We have sin2 x=1-cos2x2 Then ∫sin6x dx=∫sin2 x3dx                  =∫1-cos 2x23dx…

Q: each of the problems, solve the given differential equation. 2. y` = x2/y(1+x3)

A: Given query is to find the solution of the differential equation.

Q: I. Evaluate the triple integral zdV, where E is bounded by the cylinder y? + z? = 16 and the planes…

A: Let's find.

Q: Find the derivative of f(x) = In [sin(x) +x] Lsin(x)-x] %3D 2(sin x – x cos x) x2 - sin? x )2(x cosx…

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Q: Determine integrals for the area of the shaded region given the following figure. In part (a), give…

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Q: 9- 4x2 Evaluate: xp-

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Q: A/ Certain values of x and log1o x are (300, 2.4771), (304, 2.4829), (305, 2.4843) and (307,…

A: Note: As per our company guidelines we are supposed to answer the first question only. Kindly ask…

Q: Determine whether the following series converges. Justify your answer. 00 3k° +k Σ 2k° - 2 k = 1

A: To determine whether the given series is convergent .

Q: smoving along the graph of the given function at the rate ax/dt. Find dy/dt for the given v - = 2x +…

A: Given query is to find the value of indicated derivative.

Q: x2+64 Using trigonometric substitution, given dx, the simplified form of the integral is: x2 sec Odo…

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Q: Given (x + 4)(x – 2) f(x) = x2 —2(х — 8) - f'(x) = x3 4(х — 12) f"(x): - x4 (a) Find the domain of…

A: As per our guidelines we are supposed to answer only first three parts. Kindly repost others part as…

Q: Type your answers in the following order and format: a=1,b=2. DO NOT include spaces in between…

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Q: 2X + Y+ 6z= 9 8X + 3Y + 2Z= 13 X + 5Y + Z= 7 X=2 Y=4 Z=15 O X-1 Y=1 Z=1 O X=1 Y=2 Z=1 O X=4 Y=2 Z=-7…

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Q: 1) Ifféx) =x + 5 and g(x) = x² -3, then find g(Ư(0) . 2) Iffés) = secx, and g(x) = L, then find…

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Q: 9 – 4.x² -dx Evaluate: 9 – 4.x² – 2 sin () +C A f (x) = - B /9 – 4.x² + 2x sin- () +C f (x) = f (x)…

A: ∫9-4x2x2dx

Q: The integral 4 dy dx is equal to: Select one: 12 6. None of them

A: To determine the value of the integral ∫03∫014 dy dx.

Q: If a ball is given a push so that it has an initial velocity of 24 ft/sec down a certain inclined…

A: Given problem:- If a ball is given a push so that it has an initial velocity of 24 ft/sec down a…

Q: If f(x) = x'+ 3x + 4x + 5 and g(x) = 5; find g(f(x)) %3D %3D O 5x? + 15x² + 20x + 25 O 5x² + 15x +…

A: Topic = Functions As per guidelines , At  a time only one question can be answered. please repost…

Q: dx Evaluate: xV x2 +4 (A None of the given choices ® n Vx2+4- 2 + C x² + 4 +2 Vx²+4-4 +C x² + 4 + 4…

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Q: In each of the problems, solve the given differential equation. 1. y` = 1 + x + y2 + xy2 2. y` =…

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Q: Find the inte gral. Box Final Answec For the definite integral, give the exact answer only r se?- gE…

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Q: 4. Find the area of the region that lies under the graph of f over the given interval. a. f(x) = 2 -…

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Q: dy 1 y? +y 3

A: We have to integrate.

Q: x dy Q33. Solve the differential equation = 3x dx (a) y =+ ce 5 (b) yà = +ce 5 +ce 5 (c) yš = Vx +…

A: To solve the differential equation xy-23dydx+35y53=3x.

Q: Evaluate the integral. .V3/2 35x2 dx V1- x2

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Q: 1 * cot³. CSC2 x3 x2

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Q: Sketch the region of integration and change the order of integration for the integral 9. / | (x, y)…

A: First we sketch the region of integration then change the order of integration.

Q: csc 2 5x cot 5x dx, can be evaluated conveniently using Trigonometric Transformation. ( A) True…

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Q: e auxiliary equation of the DE: sy"-4 y"+ -2 y=0 is s m3-4 m2+-2 =0. Lect one: True False

A: We have to choose the correct option from the given options

Q: wo linearly independent solutions of the differential equation y"-4 y=0 are O y,=e** and y, = e 4x…

A: I am attaching image so that you understand each and every step.

Q: dx = x +C 3. 45x dx = -5x +C 4. 12V dx =-x+2x' +C 4x + 35x 4. 4 +8x dx = -5xi +C 4 28x 15x dx = 4x+-…

A: The integration of the integral  35x3/4/4 +8x-3.

Q: 3. Find dy/dx x = Vy + Vỹ 1 + Vx 4. Find the second and third derivative of y = 5. Find dy/dx y =…

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Q: Determine if the equation is separable. If so, solve the initial value problem. " e'y'(t) = t (In…

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Q: + c2e4x The auxiliary equation of a second-order homogeneous linear differential equation is m - 7m…

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Q: Let A = (1, -2) and B = (6, 2). Solve for projyA. %3D

A: projBA  implies projection of A on the vector B. projBA =A·BB2 B  ............(1) A·B is dot product…

Q: y' = et ; y(0) = 2 find the general solution

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Q: Consider the function below defined on the indicted interval. f(x)= -(10x+x^2), [-10,0] Find the…

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Q: d d Calculate [ri(t) · r2(t)] and r1(t) × r2(t)] first by differentiating dt dt the product directly…

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Q: The general solution of the second-order linear homogeneous differential equation y" +6 y=0 is y=…

A: Let's find.

Q: If D is the region in the third quadrant between x +y? = 1 and x2 + y? = 4, then using the polar…

A: We have to convert given double integration into polar coordinates integration.

Q: Use a triple integral to find the volume of the given solid. The tetrahedron enclosed by the…

A: Given that the tetrahedron enclosed by the coordinate planes and the plane 7x+y+z=4.

Q: Find the values of a and b for the curve x'y+ay =b if the point (1,1) is on its graph and the…

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Q: Let R be the region bounded by y =x+4, y=0, and x=4. Draw the region R, and evaluate the following…

A: Let's find.

Q: 5xy = 4x²z – 3yz²; yx and yz- %3D Z.

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Q: (Continue) An astronaut drops a hammer from rest a vertical distance of 2.0 meters above the surface…

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Q: A point is moving along the graph of the given function at the rate dx/dt. Find dy/dt for the given…

A: We can find the answers as below.

Q: Su Find D. andR %3D

A: Domain is the set of input values for which the function is defined. Range is the set of output…