第9讲 积分 视频课程
第9讲 积分
视频时长
50 分钟
建议学时
5-6 小时
语言
中文
由于视频文件较大，加载可能需要几分钟。感谢您的耐心等待。
学习目标
- Understand integration as the reverse process of differentiation (indefinite integrals) and find antiderivatives.
- Evaluate definite integrals and understand their interpretation as the signed area between a curve and the -axis.
- Apply both parts of the Fundamental Theorem of Calculus.
- Integrate functions of the form (for rational ) and sums/differences of such functions, including those requiring prior simplification.
- Utilise properties of definite integrals, such as linearity and combining integrals over contiguous ranges.
- Calculate the area of regions bounded by curves and lines.
- Approximate definite integrals using the trapezium rule and assess whether the approximation is an overestimate or underestimate.
- Solve simple first-order differential equations of the form by direct integration.
