Senior Secondary (HKDSE) · Mathematics M2 (Algebra and Calculus)

Indefinite integration and its applications: Practice Questions

5 multiple-choice questions marked as you go, and 5 written questions with worked solutions. All on Indefinite integration and its applications.

10 questions24 marksFree, no account

Question 1

1 mark

Evaluate the indefinite integral: $$\int \left( 5x^4 - \frac{3}{x^2} \right) dx$$

Question 2

1 mark

Evaluate the indefinite integral: \( \int \frac{\ln x}{x^2} \, dx \).

Question 3

1 mark

Evaluate the indefinite integral: \( \int x^3 e^{x^2} \, dx \).

Question 4

1 mark

Evaluate the indefinite integral:$$ \int \frac{e^x}{1+e^{2x}} \, dx $$

Question 5

1 mark

Evaluate the indefinite integral:$$ \int \sin(\ln x) \, dx $$

Question 6

2 marks

Find the indefinite integral of the function \(f(x) = 5x^4 + 2\sin x\) with respect to \(x\).

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

Question 7

4 marks

Evaluate \(\int x e^{2x} \, dx\) using integration by parts.

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

Question 8

5 marks

Evaluate the indefinite integral: $$ \int x \arctan x \, dx $$

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

Question 9

3 marks

The marginal cost of producing \(x\) units of a product is given by \(C'(x) = 6x^2 - 2e^x\). If the fixed cost (cost when \(x=0\)) is \( \$100 \), find the total cost function \(C(x)\).

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

Question 10

5 marks

Evaluate the indefinite integral \( \int \arcsin x \, dx \).

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

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