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) $\int_0^2 x^4 \, dx$