3) Let R be the region in Q1 bounded by the graphs of these equations: y =16-x²,y=-4x+16 Sketch R on a set of coordinate axes. Mark the two "tip" points of R with their coordinates. а) Find the exact Area of R by integrating with respect to the x - axis (vertical rectangles). b) c) Set up – but do not evaluate - the definite integral that would represent the Area of R when integrating with respect to the y- axis (horizontal rectangles).

Q: b) Express the area of the pool, A in terms of I and r. c) Hence, or otherwise show that A = -² +…

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Q: i) ii) The following two functions are given: y = x and y = x¹. Sketch the two curves on the same…

A: Topic = Application of integration

Q: 1) a) Find and -1 b) Using a graph, explain why the first integral in (a) gives the area, whereas…

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Q: From a 24-cm by 24-cm piece of cardboard, square corners are cut out so that the sides can be folded…

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Q: 28, g6) = 2x2 [,3],8 reclanyles

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Q: a. Using three approximating rectangles and midpoints, find the approximate area under the curve of:…

A: The given function  , The midpoint rule

Q: b) Express the area of the pool, A in terms of I and r.

A: We need to solve the part (b) of the question :

Q: Consider the curves x = 12y? and x + 6y = 18. a) Determine their points of intersection (x1, Y1) and…

A: Given :   x=12y2 x+6y=18

Q: 1)Find the area bounded by the given curves: a)y = 6x2 and y = 24   b)y = 3x2 − 12 and y = 0

A: The given function are y=6x2 and y=24. The area bounded by the given curves as shown below:

Q: y =Ax) If 78 9 10 1I -11 Use the graph and the notion of signed area to evaluate the definite…

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