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解题方法
1 . 若关于
的二项式
的展开式中各项的系数和为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4904f9ba87703283e13a44f3823b6758.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2466748f730da3899ef46d3e0410a98f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c1dfc770fc27e0b9bf602ec2f842ae9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4904f9ba87703283e13a44f3823b6758.png)
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2 . 由抛物线
与直线
及
所围成图形的面积为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0483173e47cf2f3fe427826c08d3f1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94fcf57347aec685a8fca271aba14eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb45f673c56a289ea78831c9237e8d20.png)
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3 . 知识卡片:一般地,如果
是区间
上的连续函数,并且
,那么
.这个结论叫做微积分基本定理,又叫做牛顿—莱布尼茨公式.当
,
时,有如下表达式:
,两边同时积分得:
,从而得到如下等式:
请根据以上材料所蕴含的数学思想方法,由二项式定理
计算:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7fe8f27f7d0118b645b0577c990cb9f.png)
_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4776c85b79df196f606d3ebf3697fbc3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/babadc15694ea4139b1bb919a7d49b93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2eb0e20a88409f5d7e899876d9d5ef09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c354be10f49f79ca7fdd3da9837a9b5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2079e9798470edc75b66126cf06da150.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a8306906c6ffde45231e08776c0fea7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4613b9e01d001fab00a2f288d28b782.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f303360ac002854ad3d63a5fca122e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7fe8f27f7d0118b645b0577c990cb9f.png)
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4 . 已知
,则二项式
展开式中的常数项为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecc4e97fd5fcd7d200bcbfb12fa5dfd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd7e8844bb80ddb2c97a24934f122545.png)
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5 . 已知
则
的展开式中含x的项为_____
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ccae87187c1123263335351fd4dab58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/970223cc1bb997665095e3133e0a68c1.png)
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6 . 设
,则二项式
的展开式中
项的系数是_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db3bc9597f8bea5a8c9ed020fbf086b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c10145ee48f6e60562a01e954da13cef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0a89e3c30f6e4d4c5db4378b05d987.png)
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2024高三下·全国·专题练习
7 . 已知
,那么
展开式中含
项的系数为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f5c7bee1ebd772d821b7ab529a03516.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bac4eff8dd552a713e5f509ff6a1b36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0a89e3c30f6e4d4c5db4378b05d987.png)
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8 . 设
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a36e682e4eea73c6357c3b06ff29bbdd.png)
________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77a94fd1ee96531561137dd0a48fbde9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a36e682e4eea73c6357c3b06ff29bbdd.png)
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9 . 若
,则在
的展开式中,
的系数为__________ .(用数字作答)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e022f44a04fd377f9f1dc0b46eebd8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d135a1234ae1138f3ec2f77fe6c2954c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a6a94336d7eb3eb790a3f3521c46401.png)
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10 . 若函数
的图象是连续平滑曲线,且在区间
上恒非负,则其图象与直线
,
,
轴围成的封闭图形的面积称为
在区间
上的“围面积”.根据牛顿-莱布尼茨公式,计算面积时,若存在函数
满足
,则
为
在区间
上的围面积.函数
在区间
上的围面积是____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4776c85b79df196f606d3ebf3697fbc3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54b53b86bd516400d6fa7dabb3603f31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82b334dafda377c3db77647c8cf1e95f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4776c85b79df196f606d3ebf3697fbc3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61c388166862b3ccfcc7ca749ebe5949.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/babadc15694ea4139b1bb919a7d49b93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e92da4cc260df72ae483bc324f5ed86d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4776c85b79df196f606d3ebf3697fbc3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/368c73c5b1fc66954165a11ebd9bba5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80e820f5bf097ea09e01c936a33f1911.png)
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