MATH1011 - Lecture 12

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MATH1011 - Lecture 11
Skeleton Slides

Volume by Cross Sections

• See Volumes of Revolution

Length of a Curve

• Formula for length of a curve: $L={\int }_a^b\sqrt{1+(f^{\prime }(x){)}^2}dx$
  • See slides for proof

Numeric Integration

• Computing definite integrals by sums is called numerical integration
  • This is used when we cannot find an antiderivative for $f$
  • Thus we approximate an integral using a weighted sum of function values
• You can find some numeric integration techniques in the slides

Integration Techniques

• See Advanced Calculus Techniques and revise formula sheet