2nd Year Mathematics Chapter 3 Test03: Integration

Q1. Multiple choice questions (Attempt all · 8 × 1 = 8)

1. $\text{If } f \text{ is integrable, then it is .}$
   1. discontinous
   2. unbounded
   3. continuous
   4. linear
2. $\int \sqrt{x} \, dx$ is:
   1. $x^{3/2} + C$
   2. $\frac{2}{3} x^{3/2} + C$
   3. $\frac{3}{2} x^{3/2} + C$
   4. $x^{1/2} + C$
3. If ' f(x) = 3x² + 2x , then f(x) is :
   1. 6x + 2 + c
   2. x³ + x² + c
   3. 3x³ + 2x² + c
   4. $1.5x³ + x^2 + c$
4. ∫ sin2x dx is:
   1. $\frac{\cos 2x}{2} + c$
   2. 2cos2x + c
   3. $-\frac{\sin 2x}{2} + c$
   4. $-\frac{\cos 2x}{2} + c$
5. $\int_{\pi/6}^{\pi} \cos x \, dx$ is:
   1. $-\frac{1}{2}$
   2. $\frac{1}{2}$
   3. $\frac{3}{2}$
   4. $-\frac{3}{2}$
6. $\int \frac{d}{dx} (x^2) \, dx$is equal to:
   1. x² + c
   2. 2x + c
   3. $\frac{x^3}{3} + c$
   4. 2x - c
7. $\frac{d}{dx} \int_{-2}^{x} t^3 \, dt = x^3$ is equal to:
   1. t⁴
   2. t³
   3. x²
   4. x³ - 16
8. What is relation between $\int_{1}^{2} x \, dx \text { and } \int_{1}^{2} t \, dt$ ?
   1. $$\int_{1}^{2} x \, dx > \int_{1}^{2} t \, dt$$
   2. $$\int_{1}^{2} x \, dx < \int_{1}^{2} t \, dt$$
   3. $$\int_{1}^{2} x \, dx \neq \int_{1}^{2} t \, dt$$
   4. $$\int_{1}^{2} x \, dx = \int_{1}^{2} t \, dt$$