MCQOPTIONS
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MCQOPTIONS
This section includes 5 Mcqs, each offering curated multiple-choice questions to sharpen your Differential and Integral Calculus Questions and Answers knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
The integral of \(\int_{-1}^1 \int_0^z \int_{x-z}^{x+z} (x+y+z)\,dy \,dx \,dz\) is given by _______ |
| A. | 0 |
| B. | 1 |
| C. | 0.25 |
| D. | 4 |
| Answer» B. 1 | |
| 2. |
The integral value of \(\int_0^1 \int_0^{1-x} \int_0^{1-x-y} \frac{dz dy dx}{(1+x+y+z)^3} \) is given by_____ |
| A. | \(log\sqrt{2} – \frac{7}{16}\) |
| B. | \(log\sqrt{4} + \frac{5}{32}\) |
| C. | \(log\sqrt{2} – \frac{5}{16}\) |
| D. | \(log\sqrt{4} – \frac{6}{32}\) |
| Answer» D. \(log\sqrt{4} – \frac{6}{32}\) | |
| 3. |
The integral value of \(\int_0^{\frac{π}{2}} \int_0^{a sinθ} \int_0^r r \,dr \,dθ \,dz \) is _____ |
| A. | 0.5 |
| B. | 0.25 |
| C. | 1 |
| D. | 0 |
| Answer» E. | |
| 4. |
The integral value of \(\int_0^a \int_0^x \int_0^{x+y} e^{x+y+z} \,dz \,dy \,dx\) is given by _____ |
| A. | \(=\frac{1}{3}(e^{4a}+6e^{2a}+8e^{a}+3)\) |
| B. | \(=\frac{1}{3}(e^{4a}-6e^{2a}+4e^{a}+3)\) |
| C. | \(=\frac{1}{8}(e^{4a}-6e^{2a}+8e^{a}-3)\) |
| D. | 0 |
| Answer» D. 0 | |
| 5. |
The value of \(\int_0^1 \int_0^x \int_0^{x+y} \,xyz \,dz\, dy\, dx\,\) is given by ____ |
| A. | 17/144 |
| B. | 16/72 |
| C. | 17/72 |
| D. | 15/144 |
| Answer» B. 16/72 | |