Integration exam questions
Exam-style Integration questions with worked solutions, step-by-step methods and common student mistakes. Practice for Mathematics and other qualifications.
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What to know for Integration questions
Integration reverses differentiation and accumulates quantities. Questions include indefinite integrals, definite integrals, areas, differential equations and motion from velocity or acceleration.
Increase each power and divide by the new power when the power rule applies. Include a constant for an indefinite integral, but use limits for a definite integral and interpret negative signed area carefully.
A reliable exam method
- Simplify the integrand and choose the appropriate rule or substitution.
- Integrate term by term, adding + c when there are no limits.
- For definite integrals, substitute upper then lower limit; use boundary conditions or geometry where the context requires it.
StudyVector example questions
Try these Integration questions
Answer ALL questions. Write your answers in the spaces provided.
Find ∫ (6x² + 4x) dx.
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2x³ + 2x² + c. Remember the constant of integration.
(Total for Question 1 is 3 marks)
Evaluate ∫₁² 3x² dx.
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[x³] from 1 to 2 = 8 − 1 = 7.
(Total for Question 2 is 3 marks)
Given dy/dx = 4x − 3 and the curve passes through (2, 5), find y in terms of x.
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Integrate: y = 2x² − 3x + c. Using (2, 5): 5 = 8 − 6 + c, so c = 3 and y = 2x² − 3x + 3.
(Total for Question 3 is 4 marks)
Question and worked solution
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Tutor explanation
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