Consider the function $f(x) = e^{-x^2}$ defined on the interval $[0, 2]$.
(a) Explain how the definite integral $\int_{0}^{2} e^{-x^2} dx$ can be interpreted as the limit of a Riemann sum.
(b) Determine the number of trapeziums required to approximate the definite integral $\int_{0}^{2} e^{-x^2} dx$ using the trapezium rule such that the absolute error is less than 0.01. Justify your answer. (Note: You do not need to calculate the approximation, just determine the required number of trapeziums)
Marking your answer...
This may take a few seconds
Sign up for free to see your full marking breakdown and personalised study recommendations.
Create Free Account Log inThis is a free VCE Units 3 & 4 Mathematical Methods practice question worth 6 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
All free, all instant AI marking.
StudyPulse has thousands of VCE Mathematical Methods questions with full AI feedback, mark breakdowns, progress tracking, and study notes across every Key Knowledge point including Definite Integral as Limit.
