2. SET-UP the definite integral that will give the area of the region the variable of integration and (b) y as the variable of integration 3 y = -x 1 x = -Vy+2 y = -1

Q: a) Evaluate x In (2.x) dx by using integration by parts b) Find the area bounded by the curve x- 3+…

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Q: 3. Find the area of the region in the first quadrant that is bounded above by y = vx and below the…

A: Solution

Q: 10. Find the area bounded by y = x and x² – 2х — у %3D 0. -

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Q: 1) Use a double integral to find the area of the region enclosed by y= x² and y = 2x.

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Q: Use an iterated integral to find the area of the region bounded by the graphs of the equations. y =…

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Q: Use an iterated integral to find the area of the region bounded by the graphs of the equations. y =…

A: Given the equations are y = x32 y = 6x

Q: If a horizontal element is used to find the area bounded by y=√x, x=4 and the x-axis, the limits of…

A: Horizontal element

Q: What is the area of the region bounded above by y= sin x below by y=x- T and from the left by the…

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Q: 2.4\(a)Use a double integral to determine the volume of the region formed by the intersection of the…

A: Volume between cylinders using double Integrals

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: 1. Consider the region R bounded by y = sin x, y = cos x,x = and x = Set up the integral that will…

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Q: 4) Find the area of the region bounded by the given curves. a) y = sin(x) cos(x) and y = sin(x) , 0…

A: Since you have asked multiple questions in single request so we  will be answering only first…

Q: Sketch the region whose area is given by the definite integral. 36 - x2 dx y y 12 35 30 25 20 15 10…

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Q: Use an iterated integral to find the area of the region bounded by the graphs of the equations. y =…

A: The given curves are y=36-x2   and   y=x+6. Sketch the region bounded by these two curves as shown…

Q: Find the area of the region bounded above by y = sin(x) and below by y = cos(x 2 1.5 4 0.5+ X

A: Using horizontal /vertical strip

Q: Use an iterated integral to find the area of the region bounded by the graphs of the equations. y =…

A: The equation is given as , y=49-x2y=x+7 find the area of the region.

Q: If a horizontal element is used to find the area bounded by y=√√x, x=4 and the x-axis, the limits of…

A: we have to find limit of function  here function is given y = x x =4 and x axis  x axis means x = 0…

Q: se a double integral to find the area of the specified region. y y = 1 8 21

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Q: i) Sketch the region of integration of the integral SS x*e*y dxdy and evaluate the integral.

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Q: Sketch the region R whose area is given by the iterated integral. * 64 – y² dx dy 60- 50- 40- 30- 20…

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Q: Use an iterated integral to find the area of the region bounded by the graphs of the equations. y =…

A: The solution is:

Q: 4. Find the area of the region bounded by y = sin x and y = sin? x between a = 0 and a =

A: The region bounded by y=sinx and y=sin2x between x=0 and x=π2 Note:    Multiple questions are given,…

Q: y. x= y? – 2 y = 1 x= e" y =-1

A: Given the graph of a region

Q: Set up the definite integral that gives the area of the region. Yı = (x – 7)3 Y2 = x – 7 dx J6 y 1.5…

A: Given problem:- Set up the definite integral that gives the area of the region. Y1 = (x-7)³ Y2 = x -…

Q: Identify the integral with Type I region between S 2ny dx dy and S 2ny dy dx g(y) g(x) and compute…

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Q: 3. Find the area of the region enclosed by y = 2 sin x, y = sin 2x, and 0 <x < T.

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Q: Set up the definite integral that gives the area of the region. Yı = 7(x³ – x) Y2 = 0 dx y 3 2 -1.5…

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Q: integrate ƒ over the given region. ƒ(x, y) = 1/(xy) over the square 1&lt;=x&lt;= 2, 1 &lt;=y&lt;=2.

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Q: 1 Determine the area of the region bounded by y = %3D 31 x+ and x = - (y-3)² + 4 Hint: Intersections…

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Q: 1. Find the area of the region bounded by the graphs of y = x² + 2, y = -x, x = 0, and x = 1. Hint:…

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Q: Sketch the region whose area is represented by the definite integral. ▪4 5 dx y y 6F

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Q: 3. Reduce to a Calc A (single variable) integral: (x+ y)dA R where R is the first quadrant region…

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Q: 1. Find the area of the shaded region by (a) integrating with respect to x and (b) integrating with…

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Q: *** If vertical element is used to find the area bounded by y=/x, x = 4 and the x – axis, the lower…

A: When a vertical element is used, it means that the area to be found is made of small such vertical…

Q: 4. Find the area bounded by the given curves:y² = x + 4, x - 2y + 1 = 0

A: Answer is given in next step.

Q: Set up a definite integral to find the perimeter of the region bounded by y = e^x, y = e^−x , and x…

A: From the given problem:   y1=ex,y2=e-x,x=1 To find the perimeter, we need to add the length of the…

Q: Set up the definite integral that gives the area of the region. Y1 = x2 – 5x Y2 = 0 dx 3 * 4 6 12,…

A: Area of the Region bounded by the curves :If f(x) and g(x) are two continuous function on a,b and…

Q: # 4. Using the known areas, find the integrals. S,(1– |x|)dx b. S',[2 + /1– x²]dx а. -

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Q: 4. Find the area enclosed by: a. y= sin(x) and y = cos(x), x= 0, x = and the y-axis.

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Q 3:- Set up an integral that can be used to determine the area of the bounded region by the gra of…

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Q: 7. Sketch the region of integration, and evaluate the integral. 2 2x r SS S- zdz de dr

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Q: Sketch the region enclosed by y=e^4x, y=e^9x , and x=1x=1. Decide whether to integrate with respect…

A: Given:   y=e^4x, y=e^9x   x = 1

Q: 7. Sketch the region of integration, and evaluate the integral. 22л г JI * zdz d0 dr 0 л 0

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Q: A region is bounded by the y=x² and y=6x-x2, Which of the following integrals would approximate the…

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Q: Set up the definite integral that gives the area of the region. Y1 = x2 + 2x + 4 Y2 = 2x + 8 dx -2

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Q: Set up the definite integral that gives the area of the region. Yı = 3(x3 - x) Y2 = 0 xp y 1.5 1.0…

A: We can see that the graph of y1 is symmetric. It made two equal areas on both sides of the y-axis.…

Q: Set up the definite integral that gives the area of the region. Y1 = x2 + 2x + 5 Y2 = 2x + 30 %3D…

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Q: If a horizontal element is used to find the area bounded by y=√x, x=4 and the x-axis, the limits of…

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Q: Set up the definite integral required to find the area of the region between the graph of y = x² –…

A: Area can be found as below :

Q: (3) Determine the region of integration first and then evaluate the integral 1-r dr dy (x – y + 1)dz…

A: To determine :-  The evaluation of the given integral .