[x xf (x²) dx Which integral is equivalent to the one shown: Oa) f f(u) du √uf (u) O b) S 2 O c) [ f(u) d 2 Od) √ √uf(u) du du du

Q: Find the surface area generated b rotating the portion of the parabolic arc x = y^2 from x = 0 and x…

A:

Q: 4. Let f(x)= a(7-a2) for all a 0 (a) Find, in terms of a, the equations of the lines tangent to…

A: Given.

Q: * (sin(2a) + cos(2x)) da Jo

A:

Q: Find the volume of the sould generated by revolving the area bounded by the _given curves about the…

A: Let's find volume of solid (V) = ?

Q: = t² - 6t + 8, The velocity function of a particle moving along a horizontal line is given by v(t)…

A: Velocity and acceleration

Q: Find the volume of the solid that results when the region enclosed by y = √√√x, y 0, and x = 49 is…

A:

Q: Evaluate the following integrals 2x ·S- -dx 2 5+2x+x

A: We know that ∫duu = lnu+C ∫1v2+a2dv = 1a·tan-1va+C

Q: Find y'. Show the step-by-step solution. Simplify your answer. 2x 1. y = In 4x²-1 2. y = log(tan x³)…

A:

Q: 3. A particle is moving along a horizontal line such that its velocity in m/s is given by v(t) = 2t²…

A:

Q: What is the integral of (2 sec^2x - sinx) dx? * O 2 cosx+tanx + C 2 tanx + sinx + C 2 tanx + cosx+C…

A:

Q: Find the derivative of the function. g'(t) = g(t) = (8t + 8)² (8t² – 8)−3 -

A: We need to find derivative of given function.

Q: 3. S. 3*sech³ (3³) 1+tanh (3*) -dx

A:

Q: 9 To express Q(x) = cos(4x-5) as the composition of three functions, identify f, g, and h so that…

A: The given function is  Q(x)=cos9(4x-5).

Q: The following differential equation is a Bernoulli equation: 2 dy = y³ where y = f(t) dt t By making…

A: To convert into linear differential equation.

Q: 3. Find the area bounded by a parabola and any right chord (use the parabola y2 = 4ax, chord x = x₁)…

A: In this question, we want to find the area bounded by the parabola and a right chord.

Q: (6) Sketch a graph of a function, f, that has the following properties: • lim f(x) = 3 and lim f(x)…

A: Given information:  ----------------------------------------------------------------------------…

Q: S 1 C=S²x + Sin'x

A:

Q: cos³ 3x sin 3x dx

A:

Q: Find the volume of the solid that results when the shaded region is revolved about the indicated…

A: Given :y=9-2x0<y<8revolution about y-axis

Q: 1. Why is it important to use the six trigonometric ratios in getting a missing angle value?

A: The six trigonometric ratios are sine, cosine, tangent, cotangent, secant, and cosecant. Basically,…

Q: Find the area of the surface generated by revolving about the x-axis the ellipse x = acost, y =…

A: We need to find area. NOTE - As per Bartleby's guidelines we can solve one question from multiple…

Q: Solve for C using the form f(x,y)=C. Given [2x + ycos(xy)] dx + x cos(xy)dy = 0; f(1)=pi/6. 1…

A: We use the concept of exact differential equations to find the general solution to given…

Q: Set up the triple integral that will give the following: the volume of the solid B that lies above…

A: We have to set up the integral and draw solid B.

Q: 2x x→∞ 3x² +5 3x xx√√√x² x² +4 X lim x→→∞ 2 sin î (a) lim (b) lim (c)

A: Given

Q: sinhr²-² 2 1. lim r+0 sinhr−r

A: To evaluate: limx→0 sinh⁡x2−x2sinh⁡x−x Given limit is of 00 form L'Hospital's rule tells us that if…

Q: Evaluate the limit using the L'Hopital's Rule 1 - cosh x lim x+0+ ln(x² + 1)

A: SOLUTION-

Q: The position of the sun at sunset, north or south of due west, depends on the latitude and the day…

A: We need to solve sinusoidal problem.

Q: Find the point(s) on the hyperbola x^2 - y^2 = 2 closest to the point (0, 1).

A:

Q: ab c Pq r U V W a. det (2B¹) where B = 4u 2a 4v 2b -q 4w 2c <-r 2p -a+u 3u b. det (20¹) where C =…

A: Given problem:-

Q: Kindly write this, I cant understand by text

A:

Q: 3. (x³ - 4)dx x3 + 2x² + 2x S

A: Given, ∫x3-4x3+2x2+2xdx

Q: Perform the integration. (sinh x)(coth→ x + csch3x) dx

A: A detailed solution is given below.

Q: Question Eight y s 8 7 5 4 14 4 3 -2 -1 The diagram shows the shaded region bounded by the curves y…

A:

Q: What is the center of gravity of the solid formed when the plane region bounded by y = x^2 and y=x+2…

A: We sketch the given region using a graphing calculator as shown below:   The shaded region is…

Q: f(x) = 4√√x + 2x¹/2 - 8x-7/8 +x². f(x) +2 1 x3 = ²325/2 - 2x³/2+1/32²³- x³ - 2x² + x −1. 9

A:

Q: २ -2 el dy ely +2 e. 2

A: To integrate.

Q: Σ(;). Since the series can be rewritten in the form 4 a = r= it is a geometric series with:

A:

Q: 1.) +y=e+ dx=3e-t 2. .) d- given: x(0) = 0, y(0) = 1 dy-x=0 d+y=1 given a z (0) = -1, y(0) = 1.

A:

Q: Evaluate the multiple integral. * 131-x² SS S dz dy dx 100 0 2/3 5/3 4/3

A:

Q: Determine the order of the given differential equation and state whether the equation is linear or…

A:

Q: (1) Prove that the product xy of two real numbers x and y is nonnegative if and only if the absolute…

A:

Q: What is the volume in cubic units of the solid formed when the region. bounded by y = x^2 + 1, y-…

A: Given :y=x2 + 1, y-axis , x-axis and x=2 is revoloved about x=-2.Formula :Volume in…

Q: Which statement is true for a function f(x)? b The average value of a function is [ f(x) dx. a f…

A:

Q: A particle is moving along a horizontal line such that its velocity in m/s is given by v(t) = 2t²…

A:

Q: What is the volume in cubic units of the solid formed when the region bounded by x = y - y^2 and x =…

A:

Q: Find the solution of the given initial value problem in explicit form. 1 y' = (1-7x)y², y(0) = 6…

A:

Q: Perform the integration. (sinh x)(coth? x + csch3x) dx

A: Here is the solution:

Q: Find the volume of the colld_generated by. revolving the area bounded by the given curves_ about the…

A: We need to find volume.

Q: Question 1 Express the Laplace Transform of the following functions: (a) f(t) = 2t sin(3t) - 3te5t…

A:

Q: 6 r5 So f5x dy dx X 1

A: