Mathematics Expert Academy Logo

Mathematics Expert Academy

Raising Mathematical Champions

Hard Calculus Practice Questions

1. Evaluate ∫ (2x^3 − 5x + 4) dx

Answer: (1/2)x^4 − (5/2)x^2 + 4x + C

2. Find the derivative of f(x) = x^2 e^x

Answer: f'(x) = e^x(x^2 + 2x)

3. Evaluate lim(x→0) (sin(5x)/x)

Answer: 5

4. d/dx (ln(x^2 + 1))

Answer: 2x / (x^2 + 1)

5. Evaluate ∫ 1 / (x^2 + 4) dx

Answer: (1/2) arctan(x/2) + C

6. Find derivative: f(x) = sin(x^2)

Answer: f'(x) = 2x cos(x^2)

7. Evaluate ∫ x e^(2x) dx

Answer: (1/2)x e^(2x) − (1/4) e^(2x) + C

8. Solve d^2y/dx^2 = 6x

Answer: y = x^3 + C1 x + C2

9. Evaluate ∫ sec^2(x) dx

Answer: tan(x) + C

10. Find derivative of f(x) = ln(sin x)

Answer: f'(x) = cot(x)