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.
480 exam-style questions on AQA A Level Maths 1.11 H: Integration, covering 1.11.1 Fundamental Theorem of Calculus, 1.11.2 Integrating standard functions, 1.11.3 Definite integrals and areas, 1.11.4 Integration as the limit of a sum (A-level only), 1.11.5 Integration by substitution and by parts (A-level only), 1.11.6 Integration using partial fractions (A-level only), 1.11.7 Differential equations with separable variables (A-level only), and 1.11.8 Interpreting solutions of differential equations (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.