Question 1

Find ∫(x³ + 2x) dx.

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Question 2

The gradient of a curve is dy/dx = 6x − 4. Find the general equation of the curve.

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Question 3

∫3x² dx = ?

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Question 4

Which of the following is ∫5 dx?

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Question 5

f'(x) = 3x² − 2, f(1) = 4. Find f(x).

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Question 6

Find ∫(3x² − 4x + 1) dx and verify by differentiating your answer.

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Question 7

f'(x) = 4x and f(0) = 3. Which expression for f(x) is correct?

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Question 8

Find the area under y = 2x + 1 from x = 1 to x = 3.

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Question 9

Find the area under y = 3x from x = 0 to x = 4.

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Question 10

Find ∫[0 to 1] (2x³ − x + 3) dx.

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Question 11

Given f'(x) = 10x − 3 and f(2) = 12, find f(x).

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Question 12

A curve has dy/dx = 3x² + 2 and passes through (1, 6). Find the equation of the curve.

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Question 13

f'(x) = 4x − 1 and f(0) = 5. Find f(1).

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Question 14

Find ∫(4x³ − 6x² + 5) dx.

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Question 15

Evaluate ∫[1 to 2] (3x² − 2x) dx.

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Question 16

∫[0 to 3] (x² + 1) dx = ?

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Question 17

Given dy/dx = 6x², find y if y = 5 when x = 1.

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Question 18

∫[5 to 5] (x³ + 5) dx = ?

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Question 19

Evaluate ∫[1 to 4] 2x dx.

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Question 20

Find ∫(5x⁴ − 3x² + 8x − 2) dx.

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Topic 5.5: Integration and Antiderivatives Questions

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