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Integration: lesson checks flashcards

This deck has 7 check-yourself questions and 6 spot-the-error cards. The misconception each lesson corrects, and its check-yourself question with the worked answer. Rate each answer, and the card comes back sooner or later depending on how you rated it.

Years 12–13 · all 584 maths cards

How the five kinds differ

Standard results ask you to recall a formula or a value. Definitions ask you to state a mathematical term precisely. Recall prompts ask for a rule, condition or method. Check yourself cards are a short question with its answer. Spot the error cards ask you to correct a statement that is wrong.

Every card in this deck

Choose any card to try it in the player above. Each card links to the lesson that teaches it.

• ∫xⁿ dx = xⁿ⁺¹/(n + 1), and that is the whole answer.Spot the error
• Find ∫(4x³ + 2/x³) dx, and verify your answer by differentiation.Check
• A definite integral is an area, always.Spot the error
• Using algebra, find the exact value of ∫₀⁴ (x + 2)²/√x dx.Check
• Find the exact value of ∫₁^e (2/x) dx, and evaluate ∫₀^π/4 sec² x dx.Check
• ∫uv dx = ∫u dx × ∫v dx.Spot the error
• Find the exact value of ∫₀¹ xe^x dx.Check
• ∫ 1/f(x) dx = ln|f(x)| + c.Spot the error
• Find the exact value of ∫₀² 2/((x + 1)(x + 3)) dx, giving the answer as a single logarithm.Check
• The area between two curves only makes sense when both sit above the x-axis.Spot the error
• The curve x = 2 cos t, y = sin t for 0 ≤ t ≤ π/2 is a quarter of an ellipse. Show that the area under it is π/2.Check
• Integrate both sides, rearrange, and add the + c at the end.Spot the error
• Solve dy/dx = y² sin x, given y = 1 when x = 0, and state where the solution stops being valid.Check

The lessons these cards come from

• Areas, parametric curves and the limit of a sum
• Definite integrals and areas
• Integrating rational functions
• Integrating standard functions
• Integration as antidifferentiation
• Integration by substitution and by parts
• Solving differential equations

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