MCQOPTIONS
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MCQOPTIONS
This section includes 9 Mcqs, each offering curated multiple-choice questions to sharpen your Integral Calculus knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
The x-coordinate of the center of gravity of a plane region is given by, \(x_c=\frac{1}{M}∬xf(x,y)dxdy.\) |
| A. | True |
| B. | False |
| Answer» B. False | |
| 2. |
A sphere with the dimensions is shown in the figure. What is the error that can be incorporated in the radius such that the volume will not change more than 4%? |
| A. | 0.127% |
| B. | 0.0127% |
| C. | 12.7% |
| D. | 1.27% |
| Answer» C. 12.7% | |
| 3. |
Given \(∫_0^8x^\frac{1}{3}dx,\) find the error in approximating the integral using Simpson’s 1/3 Rule with n=4. |
| A. | 1.8 |
| B. | 2.9 |
| C. | 0.3 |
| D. | 0.35 |
| Answer» E. | |
| 4. |
What is the mass of the region R as shown in the figure? |
| A. | 8 |
| B. | 9 |
| C. | \(\frac{9}{2} \) |
| D. | \(\frac{9}{4} \) |
| Answer» C. \(\frac{9}{2} \) | |
| 5. |
Which of the following equation represents Moment of Inertia of a plane region relative to x-axis? |
| A. | ∬x2 f(x,y)dxdy |
| B. | ∬xf(x,y)dxdy |
| C. | ∬y2 f(x,y)dxdy |
| D. | ∬yf(x,y)dxdy |
| Answer» D. ∬yf(x,y)dxdy | |
| 6. |
Volume of an object expressed in spherical coordinates is given by \(V = ∫_0^2π∫_0^\frac{π}{3}∫_0^1 r cos∅ \,dr \,d∅ \,dθ.\) The value of the integral is _______ |
| A. | \(\frac{√3}{2}\) |
| B. | \(\frac{1}{√2} π\) |
| C. | \(\frac{√3}{2}π\) |
| D. | \(\frac{√3}{4} π\) |
| Answer» E. | |
| 7. |
What is the result of the integration \(∫_3^4∫_1^2(x^2+y)dxdy\)? |
| A. | \(\frac{83}{6} \) |
| B. | \(\frac{83}{3} \) |
| C. | \(\frac{82}{6} \) |
| D. | \(\frac{81}{6} \) |
| Answer» B. \(\frac{83}{3} \) | |
| 8. |
The region bounded by circle is an example of regular domain. |
| A. | False |
| B. | True |
| Answer» C. | |
| 9. |
Which of the following is not a property of double integration? |
| A. | ∬ af(x,y)ds = a∬ f(x,y)ds, where a is a constant |
| B. | ∬ (f(x,y)+g(x,y))ds = ∬f(x,y)ds+ ∬g(x,y)ds |
| C. | \(∬_0^Df(x,y)ds = ∬_0^{D1}f(x,y)ds+ ∬_{D1}^{D2}f(x,y)ds,\) where D is union of disjoint domains D1 and D2 |
| D. | ∬(f(x,y)*g(x,y))ds = ∬f(x,y)ds*∬g(x,y)ds |
| Answer» E. | |