The region is bounded by y = x³, y = 2x + 4 and y = −1. Then Area region = [ f(x) dx + √ f(x) dx + g(x) dx, where a < b

Q: Find the Critical points of the ff equation and Determine the Maximum and Minimum. - 1. y= 2x² - 12x…

A: A detailed solution is given below.

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Q: -2 What is the value of the definite integral e* dx? -4

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Q: If R is the disc with center at the origin and radius 5 then the numerical value of [xdA is equal to…

A: Please follow the next step.

Q: Which ONE of the following statements is FALSE? OA. If the function f (x,y) is maximum at the point…

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Q: Evaluate the following integral 1. y4+2y²-1 √y dy; y to 2. f(−4t + 12) (5t +15)dt

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Q: Given the function f(x, y, z) = x ln(1 − z) + following and simplify your answers. a) | fx b) u fxz…

A: We can answer both the answer as below

Q: Find the volume generated by revolving about the x-axis, the area bounded by the line 4x + 8y = 8,…

A: We need to find volume.

Q: W=-Si ; V=1-2i, W=-3-6i , U-3V+ 2W, UV, UVW, : Given U= 4-2i ; V= 3-4i atib= (utiv)w, find a ad b.…

A: Here is the solution:

Q: Evaluate the following double integral over the given region R. [[ 2 ln(x + 1) (x + 1)y Use…

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Q: The integral can be rewritten as 6u³ (a). Joudu u+1 6u4 (c). du u²+1 ܐ | dx √x+√x (b). Sū 6u² u²+1…

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Q: Find the volume generated by revolving about the x-axis, the area bounded by the line 2x + 4y = 4,…

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

Q: Hwy find the integration 3 Se vadv V 1-

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Q: The numerical value of the lim 818 n+3 nln (2) n+1 is equal to

A: We use L'Hôpital's rule to solve the limit.

Q: Use the shell method to find the volume of the solids generated by revolving the shaded region about…

A: This question can be solved using the concept of shell  method.

Q: Note: Volume of a cylinder is r²h, where is the radius and h is the height. A closed wood storage…

A: Volume of cylinder= πr^2h

Q: Eliminate the parameter 1 to find a Cartesian equation for: x = t² and y = 4 + 2t. and express your…

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Q: A rope that weighs 0.5 lb/ft is attached to a bucket filled with cement plaster that weighs 22 lbs.…

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Q: y"+y' = 0; y(0) = 0, y'(0) = 1 cost + sint t + cost + sint O B) 1- e-t t-e-t OA) OD)

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Q: Determine the intervals on which the graph of y = f(x) is concave up or concave down, and find the…

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Q: The value of the integral in terms of u is? (a). 2u³ + 6u + Arctanu + C (c). 2u³-21n|u³+1| + C dx…

A: To evaluate: ∫dxx3+x Let I = ∫dxx3+x Assuming x=u6⇒dx = 6u5du

Q: Find the area bounded by x2 = 4y + 4 and x = y 2. Using vertical element, what is the integral…

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Q: √x²-1 The value of the definite integral / dx is in the form F(b) - F(a), where a and b are the…

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Q: Given the function f(x, y, z) = x ln(1 - z) + and simplify your answers. a) fa b) fxz sin(x - 1) 2y…

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Q: Evaluate the following double integral over the given region R. 2 ln(x + 1) (x+1)y Use integration…

A: The objective of the question is evaluate the definite double integral.

Q: The domain and the range of z=cos-1(x²-y-3) are represented respectively by OAD={(x,y) ERXR: x² <y≤…

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Q: The cylindrical shell method is to be used to compute for the volume of the solid generated by…

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Q: Consider the region on the 1st quadrant bounded by y = √4x²,x and y-axes. If the region is revolved…

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Q: A manufacturer is planning to sell a total of 500 machines to both foreign and domestic firms. The…

A: Solution is here

Q: Evaluate the following double integral over the given region R. SS 4 ln(y + 1) (x + 1)(y + 1) Use…

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Q: Evaluate the following double integral over the given region R. 2 ln(x + 1) // ² dA over the region…

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Q: fu = eª₁²+₂y+a, where a, a, a3 are constants and 8² u 2² u 2² u a² + a² + a² = 1. Show that + + = U.…

A: Given problem:-

Q: 4. g(x) = (3x − 2)4; g"" (x)

A: We can find the derivatives as below

Q: Which ONE of the following statements is FALSE? OA. If f(x,y) has a saddle point at (a,b) the…

A: Maxima and minima

Q: In the partial fraction decomposition for some numbers A, B, and C. Find the value of B? -x²-x+2 C A…

A: On solving this we will get:  B= 1/2

Q: The value of x for which the series - n³(x-3)" OA. 2<x<3 or 3<x<4. O B.2<x<3 or 3<x< 4. OC. 2<x<4. O…

A: We need to find value of x.

Q: √√2₁ y = ¹, y-axis, y=1&y=3; OY

A: Volume of solid obtained by revolving region around y axis is evaluated.

Q: Consider the region on the 1st quadrant bounded by y = √4x²,x and y- axes. If the region is revolved…

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Q: The value of the definite integral fm12 √ex - 9 dx is in the form F(b) – F(a), where a In 9 and b…

A: We have to solve given Questions.

Q: +1²y=y² If the function u = ln (2¹+2²4 - v² ) then a Su rou + you is

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Q: dy Find dif: y = ln(x + √² + a² O a √2+²+² O b. √ О с. √√2²+0² O d. none of these O e √√zta

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Q: 3x at the point P (2,0, -1) in the direction The directional derivative of f (x,y,z)=ln *(x,y,z);…

A: ..

Q: The series representation of f(x) = n(x²-1) is given by power OA ¹+¹, -1<x<1. n=] } + [ B. None of…

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Q: The value of the integral in terms of u is? (a). 2u³ + 6u + Arctanu + C (c). 2u³-21n|u³ + 1| + C dx…

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Q: The tangent line to the curve at the point (1,2) also passes through d²y the point (-1,4). If at any…

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Q: Evaluate the definite integral I. 1 = [₁² [(e-x + 1) dx -1 I =

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Q: find the surface area of the portion of the curve x²+y²=4 from x=0 to x=2 when it is revolved about…

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