The function $f(x) = rac{1}{x^2 + 1}$ is defined on the interval $[0, 2]$. We wish to approximate the area under the curve of $f(x)$ on this interval using different methods.
b. Explain how the definite integral $\int_0^2 \frac{1}{x^2 + 1} dx$ can be expressed as the limit of a sum. Include appropriate notation.
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Create Free Account Log inThis is a free VCE Units 3 & 4 Mathematical Methods practice question worth 3 marks, testing your understanding of Definite Integral as Limit. It falls under Calculus in Unit 3: Mathematical Methods Unit 3. Submit your answer above to receive instant AI-powered marking and personalised feedback.
Extend introductory study of functions, algebra, calculus. Focus on functions, relations, graphs, algebra, and applications of derivatives.
Covers limits, continuity, differentiability, differentiation, and anti-differentiation.
informal consideration of the definite integral as a limiting value of a sum involving quantities such as area under a curve and approximation of definite integrals using the trapezium rule
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