Cambridge OCR A Level · Mathematics B (MEI) - H640

Integration: Practice Questions

5 multiple-choice questions marked as you go, and 2 written questions with worked solutions. All on Integration.

7 questions10 marksFree, no account

Question 1

1 mark

Calculate the area under the curve \(y = \frac{1}{x}\) between \(x = 1\) and \(x = e\).

Question 2

1 mark

Using integration by parts, evaluate \(\int x \cos(x) \, dx\).

Question 3

1 mark

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

Question 4

1 mark

Evaluate the definite integral \(\int_{0}^{2} (3x + 1)^2 \, dx\).

Question 5

1 mark

Find the integral \(\int \sin(2x) \, dx\).

Question 6

2 marks

Determine the exact value of the definite integral \(\int_{0}^{\frac{\pi}{2}} (2 \sin x + \cos x) dx\).

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

Question 7

3 marks

Find the definite integral of the function f(x) between the limits 1 and 3.
\(\int_{1}^{3} (4x^3 - 2x + 5) dx\)

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

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