MSA Education BD

 

Integration Quiz

1. What is the integral of \( \int 4x \, dx \)?

A) \( 2x^2 + C \) B) \( 4x^2 + C \) C) \( 2x^2 + 4x + C \) D) \( x^2 + C \)

2. Evaluate \( \int \cos(x) \, dx \).

A) \( \sin(x) + C \) B) \( -\sin(x) + C \) C) \( \cos(x) + C \) D) \( -\cos(x) + C \)

3. Find the integral \( \int \frac{3}{x^2} \, dx \).

A) \( -\frac{3}{x} + C \) B) \( \frac{3}{x} + C \) C) \( -\frac{3}{x^2} + C \) D) \( \frac{3x}{2} + C \)

4. What is the integral of \( \int \sqrt{x} \, dx \)?

A) \( \frac{2}{3} x^{3/2} + C \) B) \( \frac{1}{2} x^{2} + C \) C) \( \frac{2}{3} x^{2} + C \) D) \( \frac{1}{2} x^{3/2} + C \)

5. Evaluate \( \int x^3 \, dx \).

A) \( \frac{x^4}{4} + C \) B) \( \frac{x^3}{3} + C \) C) \( \frac{x^4}{3} + C \) D) \( x^4 + C \)

6. Find the integral \( \int e^{2x} \, dx \).

A) \( \frac{e^{2x}}{2} + C \) B) \( \frac{e^{2x}}{2} \) C) \( e^{2x} + C \) D) \( \frac{e^{2x}}{4} + C \)

7. What is the integral of \( \int \tan(x) \, dx \)?

A) \( -\ln|\cos(x)| + C \) B) \( \ln|\sin(x)| + C \) C) \( \ln|\tan(x)| + C \) D) \( -\ln|\sin(x)| + C \)

8. Evaluate \( \int \frac{1}{x^2 + 4} \, dx \).

A) \( \frac{1}{2} \arctan\left(\frac{x}{2}\right) + C \) B) \( \frac{1}{2} \ln|x^2 + 4| + C \) C) \( \frac{1}{2} \arctan(x) + C \) D) \( \frac{1}{4} \arctan(x) + C \)

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

A) \( \frac{x}{2} - \frac{\sin(2x)}{4} + C \) B) \( \frac{x}{2} + \frac{\sin(2x)}{4} + C \) C) \( \frac{x}{2} - \frac{\sin(x)}{2} + C \) D) \( \frac{x}{2} + \frac{\sin(x)}{2} + C \)

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