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IB MAI HL Calculus Topic 5.2 Integration (id: ee7e02641)

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admin 发表于 2024-3-18 14:40:00 | 显示全部楼层 |阅读模式
本题目来源于试卷: IB MAI HL Calculus Topic 5.2 Integration,类别为 IB数学

[填空题]
The graphs of y=-0.5 x+2.5 anl (nsr.g+8sw qd -wdod c084/q1dlg :+x o zpihc $y=0.5 x^{2}+0.5 x+1$ intersect at (-3,4) and (1,2) , as shown in the following diagrams.

1. Calculate the shaded area in diagram 1 , the area enclosed by the lines y=-0.5 x+2.5 x=-3, x=1 and the x -axis, A$_1$=   units$^2$
2. 1. Write down an integral for the shaded area in diagram 2 , the area enclosed by the curve y=$0.5 x^{2}+0.5 x+1$ , the lines x=-3 and x=1 , and the x -axis.
A$_2$=$\int_{-3}^{1}\left(0.5 x^{2}+0.5 x+a\right) \mathrm{d} x$;a=  .
2. Calculate the area of this shaded region,A$_2$≈   units$^2$
3. Hence, determine the area enclosed by the line y=-0.5 x+2.5 and the curve y= $0.5 x^{2}+0.5 x+1$




参考答案:
空格1: 12空格2: 1空格3: 6.67±3%


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