JAMB and WAEC Further Mathematics questions: Integration

16 questions with answers and explanations. Tap an option to check yourself.

1. Question 1· Integration· WAEC

   Find the area bounded by the curve y = 4 − x² and the x-axis.

   • A8 square units
   • B16/3 square units
   • C32/3 square units
   • D16 square units

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   Explanation and discussion

2. Question 2· Integration· WAEC

   Find the integral of (2x + 3)² with respect to x.

   • A(2x + 3)³/6 + c
   • B(2x + 3)³/3 + c
   • C2(2x + 3)³ + c
   • D(2x + 3)³ + c

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   Explanation and discussion

3. Question 3· Integration· WAEC

   Integrate (4x³ − 6x) with respect to x.

   • A12x² − 6 + c
   • Bx⁴ − 3x² + c
   • C4x⁴ − 6x² + c
   • Dx⁴ − 6x² + c

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   Explanation and discussion

4. Question 4· Integration· WAEC

   Find the integral of sin x with respect to x.

   • Acos x + c
   • B−cos x + c
   • C−sin x + c
   • Dtan x + c

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   Explanation and discussion

5. Question 5· Integration· WAEC

   Evaluate the integral of (3x² + 2x) with respect to x from x = 0 to x = 2.

   • A10
   • B16
   • C12
   • D8

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   Explanation and discussion

6. Question 6· Integration· WAEC

   ∫ (4x + 1) dx is

   • A4x² + x + c
   • B2x² + x + c
   • C4 + c
   • D2x + c

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   Explanation and discussion

7. Question 7· Integration· WAEC

   Find the area under the curve y = 3x² from x = 0 to x = 2.

   • A8
   • B12
   • C6
   • D4

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   Explanation and discussion

8. Question 8· Integration· WAEC

   A particle moves with velocity v = 3t² + 2 m/s. Find the distance it covers from t = 0 to t = 2 s.

   • A10 m
   • B14 m
   • C12 m
   • D6 m

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9. Question 9· Integration· WAEC

   ∫ cos x dx is

   • Asin x + c
   • B−sin x + c
   • Ccos x + c
   • D−cos x + c

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   Explanation and discussion

10. Question 10· Integration· WAEC

    The area under y = x² from x = 0 to x = 3 is

    • A6 square units
    • B27 square units
    • C3 square units
    • D9 square units

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    Explanation and discussion

11. Question 11· Integration· WAEC

    Find the integral of (x² − 4)/(x − 2) with respect to x.

    • Ax²/2 − 2x + c
    • Bx² + 2x + c
    • Cx³/3 − 4x + c
    • Dx²/2 + 2x + c

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    Explanation and discussion

12. Question 12· Integration· WAEC

    The integral of cos x with respect to x is

    • Asin x + c
    • B−sin x + c
    • Ccos x + c
    • D−cos x + c

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13. Question 13· Integration· WAEC

    Evaluate the integral of (2x + 1) from x = 1 to x = 2.

    • A6
    • B4
    • C5
    • D3

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    Explanation and discussion

14. Question 14· Integration· WAEC

    Evaluate ∫ from 1 to 3 of 3 dx.

    • A9
    • B6
    • C3
    • D12

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15. Question 15· Integration· WAEC

    The integral of 3x² with respect to x is

    • Ax³ + c
    • B6x + c
    • C3x³ + c
    • Dx² + c

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    Explanation and discussion

16. Question 16· Integration· WAEC

    Evaluate ∫ from 0 to 2 of 2x dx.

    • A8
    • B2
    • C4
    • D0

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    Explanation and discussion