Unit 5: Calculus

Topic 5.5: Introduction to Integration Questions

Practice 20 exam-style questions for IB Math AA SL Topic 5.5. Review the question stems below, then unlock the full Question Bank to access markschemes, model answers, and AI grading.

1Find2 marks

2026

Find

\int (5 - 2 x) d x

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2Find2 marks

2026

Find ∫(5 − 2x) dx.

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3Evaluate2 marks

2026

Evaluate ∫₀² (3x²) dx.

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4Find2 marks

2026

Find the area enclosed by

y = 3 x^{2}

, the x-axis, and the lines

x = 0

and

x = 2

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5Choose1 mark

Find the area enclosed by the curve

y = 4 x^{3}

, the

x

-axis and the vertical lines

x = 0

and

x = 2

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6Find2 marks

2026

Find the area enclosed by y = 3x², the x-axis, and the lines x = 0 and x = 2.

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7Choose1 mark

Find

\int (4 x^{3} - 6 x + 5) d x

, giving the general form.

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8Evaluate2 marks

2026

Evaluate

0 \int 2 (3 x^{2}) d x

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9Find2 marks

2026

Find

\int (8 x^{3} - 6 x + 1) d x

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10Find2 marks

2026

A curve has f'(x) = 6x² − 4 and f(0) = 7. Find f(x).

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11Find2 marks

2026

A curve has

f^{'} (x) = 6 x^{2} - 4

and a stationary point — wait, instead:

f^{'} (x) = 6 x^{2} - 4

and

f (0) = 7

. Find

f (x)

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12Write down1 mark

2026

Write down an expression for its area.

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13Write down1 mark

2026

Rectangles of width

1

stand on the

x

-axis. The rectangle on the interval

[k - 1, k]

has height

k^{3}

, for

k = 1, 2, 3, \dots

. Write down the equation of the curve that passes through the top-right corner of every rectangle.

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14Evaluate2 marks

2026

Evaluate ∫₁⁴ (2x + 1) dx.

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15Choose1 mark

A straight line has equation

y = 2 x + 5

. Evaluate

1 \int 3 (2 x + 5) d x

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16Write down1 mark

2026

The region between the curve

y = e^{x}

and the

x

-axis, from

x = 0

x = 2

, is shaded. Write down a definite integral that gives the area of the shaded region.

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17Evaluate2 marks

2026

Evaluate

1 \int 4 (2 x + 1) d x

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18Find2 marks

2026

Find ∫(8x³ − 6x + 1) dx.

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19Choose1 mark

A shaded region between

y = x^{2}

and the horizontal axis runs from

x = 0

x = a

and has area 72. Find

a

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20Choose1 mark

Find the area under the curve

y = x^{2}

between

x = 2

and

x = 5

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