Pearson Edexcel International A Level · Mathematics (YMA01)

Integration: Practice Questions

5 multiple-choice questions marked as you go, and 5 written questions with worked solutions. All on Integration.

10 questions23 marksFree, no account

Question 1

1 mark

Find the indefinite integral of \( \int (6x^2 - 4x + 3) \, dx \).

Question 2

1 mark

Find the exact area enclosed by the curve \(y = 4x - x^2\) and the x-axis.

Question 3

1 mark

The region \(R\) is bounded by the curve \(y = \sqrt{x}\), the x-axis, and the line \(x=4\). Find the volume of the solid generated when \(R\) is rotated through \(2\pi\) radians about the x-axis.

Question 4

1 mark

Find \(\int (6x^2 - 3x + 1) \, dx\).

Question 5

1 mark

The gradient of a curve is given by \(\frac{dy}{dx} = 3x^2 - 8x + 5\). If the curve passes through the point \((1, 4)\), find the equation of the curve.

Question 6

2 marks

Find \(\int (4x^3 - 6x^2 + 2) dx\).

Write your answer out first, then check it against the worked solution.

Question 7

4 marks

Evaluate the definite integral \(\int_0^3 (3x^2 - 2x) \, dx\).

Write your answer out first, then check it against the worked solution.

Question 8

5 marks

Find the exact area of the region bounded by the curve \(y = x^2 - 4x\) and the x-axis.

Write your answer out first, then check it against the worked solution.

Question 9

3 marks

Find the indefinite integral of \(f(x) = 6x^2 - \frac{4}{x^3} + \sqrt{x}\) with respect to \(x\).

Write your answer out first, then check it against the worked solution.

Question 10

4 marks

The gradient of a curve is given by \(\frac{dy}{dx} = 3x^2 - 8x + 5\). The curve passes through the point \((2, 1)\). Find the equation of the curve.

Write your answer out first, then check it against the worked solution.

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