Graphs are given with areas underneath them shaded. The area of the shaded regions are given and from this the value of various integrals are to be deduced.
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i <= x2; i = i+0.1) {\n dataX2.push(i);\n dataY2.push(f(i));\n }\n\n var dataX3 = [x2,x2];\n var dataY3 = [f(x2),0];\n\n dataX = dataX1.concat(dataX2).concat(dataX3);\n dataY = dataY1.concat(dataY2).concat(dataY3);\n\nvar shading = board.create('curve', [dataX,dataY],{strokeWidth:0, fillColor:colour, fillOpacity:opacity});\n\nreturn shading;\n}\n\n\n//Define your functions\nvar f = function(x) {\n return a*(x-b)*(c-x);\n}\n\n\nvar f1 = function(x) {\n return a*(c-4-b)*(c-c+4);\n}\n\nvar f2 = function(x) {\n return a*(c-3-b)*(c-c+3);\n}\n\nvar f3 = function(x) {\n return a*(c-2-b)*(c-c+2);\n}\n\nvar f4 = function(x) {\n return a*(c-1-b)*(c-c+1);\n}\n\n\n\n//Plot the graph and do shading\nboard.create('functiongraph', [f]);\n\n\n\nswitch(num) {\n case 1:\n shade(f,c-2,c+2, 'red',0.2);\n break;\n case 2:\n for (i = 0; i < 8; i++) { \n var g = function(x) {\n return a*(c-(2-0.5*i)-b)*(c-(c-(2-0.5*i))); //defining horizontal function for ith column\n }\n if (i%2 == 0) { \n shade(g,c-(2-0.5*i),c-(2-0.5*(i+1)), 'blue',0.2); 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We would like to calculate the area of the shaded region.
\n{plotgraph(a,b,c,1)}
\n\nYou will learn how to do this in Maths 2 (using so-called integration), but for now we will just estimate the area. We do this by calculating the area of the strips in the diagram below:
\n{plotgraph(a,b,c,2)}
\n\nTo save you scrolling, the function was $v(t) =\\simplify{{a}(t-{b})*({c}-t)}$.
\n(i) What are the coordinates of the points A and B?
\nA. [[0]]
\nB. [[1]]
\n\n(ii) Determine the total area of the strips. Do this by determining the area of each strip and adding them together. Remember to do simple estimates to check for big errors.
\nTotal area of columns = [[2]]
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\nIt is easy to make a little mistake, and a single mistake will result in an incorrect answer. As much as possible, find ways to check for mistakes e.g. you can make rough estimates of the length of each strip from the graph.
\n(If you have studied integration before and you want a challenge, calculate the exact area of the original shaded region and check it is similar with this estimated value.)
", "statement": "This is a calculator question.
", "tags": [], "contributors": [{"name": "Lovkush Agarwal", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1358/"}]}]}], "contributors": [{"name": "Lovkush Agarwal", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1358/"}]}