Part II. Application of the definite integral on plane areas. Situation: For the area bounded by the curve y + 2x – 2y – 3 = 0 and the y-axis, determine the following: 1. The positioning of the curve and the direction of the opening of the curve. 2. The vertex of the curve. 3. The graph of the boundary of the curve and the y-axis. 4. The area bounded by the curve and the y-axis in square units.

Q: The base of a tank is a circle, represented by x2 + y2 = 4 (in feet). The side of the tank is…

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Q: The boundaries of the shaded region are the y-axis, the line y = 1, and the curve y = √. Find the…

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Q: Find the area of the region bounded by the X – axis, the lines x = 4 and x = 6 and the curve X – 1 A…

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Q: Determine the surface area generated when a portion of the curve in the 1st quadrant of y² = 4(x² −…

A: When a curve  described by the function x=g(y), a≤y≤b  rotated about the y−axis, Then the area of…

Q: 1. Find the intersections between the curve y=√√3-x and line y+1-x=0 (a) Sketch the region R bounded…

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Q: (Challenging): Curve y =x*(x+3) is calleo Tschirnhausers cubic. Graph this at desmos.com/cal.cuator.…

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Q: y = } + sxs1 <x<1 2

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Q: For each problem, sketch the region bounded by the graphs of the functions and find the area of the…

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Q: Let the region R be the area enclosed by the function f(x) = 2x³ , the horizontal line y = –3 and…

A: Given the region R be the area bounded by fx=2x13,y=-3,x=0,x=3. Visualize the solid: Each…

Q: Given a shade region, bounded by the line y + x = 5 and the curve x² = y − 3. a. Sketch the line and…

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Q: 1. Find the surface area generated by rotating the curve y = /2x + 4 about the x-axis for x = 2 to x…

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Q: Calculate the surface area if the curve y = 3sqrt(x) is rotated about the x-axis.

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Q: The surface defined by z = f(x, y) = 2x + y hovers above the region defined by the graphic below.

A: For the given surface  F(X,y)=2x+y The region bounded by curves is shown in figure  To find the…

Q: Find the area contained between the line y = x and the curve y = x².

A: The line is y=x and the curve is y=x2

Q: Calculate the area of the smaller region (to the left of the parabola) bounded by (x+5)²=2y, the…

A: Find the slope of the tangent to the curve x2+y2=25 at (3,4). 2x+2ydydx3,4=0dydx3,4=-xydydx3,4=-34

Q: Calculate the area of the smaller region (to the left of the parabola) bounded by (x + 5)² = 2y, the…

A: The shaded region is our required area