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$\\int^{\\var{x12}}_{\\var{x11}}\\simplify{{a1}*x + {b1}} \\, \\textrm{d}x$

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$\\int^{\\var{x11}}_{\\var{x12}}\\simplify{{b1}*x + {a1}} \\, \\textrm{d}x$

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-$\\int^{\\var{x12}}_{\\var{x11}}\\simplify{{a1}*x + {b1}} \\, \\textrm{d}x$

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$\\int \\simplify{{a1}*x + {b1}} \\, \\textrm{d}x$

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$\\int^{\\var{x22}}_{\\var{x21}}\\simplify{{a2}*x^2 + {c2}} \\, \\textrm{d}x$

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$\\int \\simplify{{a2}*x^2 + {c2}} \\, \\textrm{d}x$

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$\\int^{\\var{x32+2}}_{\\var{x32}}\\frac{1}{2}\\simplify{(x-{a3})*(x-{b3})} \\, \\textrm{d}x$

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$\\int^{\\var{x42+2}}_{\\var{x41}}f(x) \\, \\textrm{d}x$

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$\\int^{\\var{x42}}_{\\var{x41}}f(x) \\, \\textrm{d}x - \\int^{\\var{x42+2}}_{\\var{x42}}f(x) \\, \\textrm{d}x$

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(i) {plotgraph(1,x11,x12,-1,10,a1,b1,0)}

This is the graph of the function $f(x) = \\simplify{{a1}*x+{b1}}$.

Which integral corresponds to the area of the shaded region? [[0]]

(ii) {plotgraph(2,x21,x22,-5,25,a2,0,c2)}

This is the graph of the function $f(x) = \\simplify{{a2}*x^2+{c2}}$.

Which integral will calculate the area of the left region? [[1]]

Which integral gives the total area of both shaded regions? [[2]]

(iii) {plotgraph(3,x31,x32,-3,7,a3,b3,0)}

This curve has equation $y = \\frac{1}{2}\\simplify{(x-{a3})*(x-{b3})}$.

Which integral gives the area of the left shaded region? [[3]]

Which of these calculates the total area of the two shaded regions? [[4]]

(iv) {plotgraph(4,x41,x42,-3,7,a4,b4,c4)}

This is the graph of some function $f(x)$.

Which of the following gives the total area of the shaded regions? [[5]]

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See Lecture 13.3 and 13.5 for background and examples.

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Graphs are given with areas underneath them shaded. The student is asked to select the correct integral which calculates its area.

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This is a non-calculator question.

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