Four students, Alice, Bob, Clara, and David are attempting to find the indefinite integral
∫ex dx \int e^x \, dx ∫exdxEach of the students' proposed results is shown below:
Alice: ∫ex dx=ex\int e^x \, dx = e^x ∫exdx=ex
Bob: ∫ex dx=Cex\int e^x \, dx = C e^x ∫exdx=Cex
Clara: ∫ex dx=ex+k\int e^x \, dx = e^{x+k} ∫exdx=ex+k
David: ∫ex dx=ex+c\int e^x \, dx = e^x + c ∫exdx=ex+c
Explain what is wrong with Alice's answer.
Explain what is wrong with Bob's answer.
Explain why Clara and David's answers are equivalent for certain values of the constants.
864 exam-style questions on Edexcel A Level Maths Integration, covering 11.1 Integrating Standard Functions, 11.2 Integrating f(ax + b), 11.3 Using Trigonometric Identities, 11.4 Reverse Chain Rule, 11.5 Integration by Substitution, 11.6 Integration by Parts, 11.7 Partial Fractions, 11.8 Finding Areas, 11.9 The Trapezium Rule, 11.10 Solving Differential Equations, and 11.11 Modelling with Differential Equations. Each one has a worked solution and a mark scheme showing where the marks go.