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) \( x^2 + C \)

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

15. 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) \( \frac{1}{2} x^{3/2} + C \)

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

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

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

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

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

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

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

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

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

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

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

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

7. In the integration by parts formula, \( \int u \, dv = \):

a) \( uv - \int v \, du \) b) \( uv + \int v \, du \) c) \( vu - \int u \, dv \) d) \( uv - v \, du \)

8. The integral \( \int \cos^2(x) \, dx \) can be solved using:

c) Trigonometric identities a) Substitution method b) Partial fractions d) Integration by parts

9. What is the integral of \( \int \frac{1}{x^2 + a^2} \, dx \)?

a) \( \frac{1}{a} \tan^{-1}\left(\frac{x}{a}\right) + C \) b) \( \frac{1}{a} \sin^{-1}\left(\frac{x}{a}\right) + C \) c) \( \frac{1}{a} \ln\left(x + a\right) + C \) d) \( \frac{1}{a} \cos^{-1}\left(\frac{x}{a}\right) + C \)

10. The integral \( \int e^{2x} \, dx \) is:

a) \( \frac{1}{2} e^{2x} + C \) b) \( 2e^{2x} + C \) c) \( \frac{1}{e^{2x}} + C \) d) \( e^{2x} + C \)

### Definite Integrals

11. The definite integral \( \int_0^1 x^2 \, dx \) equals:

a) \( \frac{1}{3} \) b) \( \frac{1}{2} \) c) \( 1 \) d) \( 0 \)

12. If \( \int_a^b f(x) \, dx = F(b) - F(a) \), then \( F(x) \) is:

c) The antiderivative of \( f(x) \) a) The derivative of \( f(x) \) b) A constant d) The inverse of \( f(x) \)

13. The definite integral \( \int_{-\pi}^\pi \sin(x) \, dx \) is:

a) \( 0 \) b) \( 2 \) c) \( -2 \) d) \( \pi \)

14. The area under the curve \( y = x^2 \) from \( x = 0 \) to \( x = 2 \) is given by:

a) \( \int_0^2 x^2 \, dx \) b) \( \int_0^2 2x \, dx \) c) \( \int_0^2 x^3 \, dx \) d) \( \int_0^2 x^4 \, dx \)