MCQOPTIONS
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MCQOPTIONS
This section includes 4 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 value of ∬R sin(x2 + y2) dx dy where R is the region bounded by circle centered at origin with radius r=2 is _____ |
| A. | πcos 4 |
| B. | π(1-cos 4) |
| C. | π |
| D. | π(1-sin 4) |
| Answer» C. π | |
| 2. |
If double integral in Cartesian coordinate is given by ∬R f(x,y) dx dy then the value of same integral in polar form is _____ |
| A. | ∬P f(r cos θ, rsin θ)dr dθ |
| B. | ∬P f(r cosθ, r sinθ)rdr dθ |
| C. | ∬P f(r cosθ, r sinθ) r2 dr dθ |
| D. | ∬P f(r sinθ, r cosθ)dr dθ |
| Answer» C. ∬P f(r cosθ, r sinθ) r2 dr dθ | |
| 3. |
The value of ∬R (x-y)2 dx dy where R is the parallelogram with vertices (0,0), (1,1),(2,0), (1,-1) when solved using change of variables is given by____ |
| A. | 16/3 |
| B. | 8/3 |
| C. | 4/3 |
| D. | 0 |
| Answer» C. 4/3 | |
| 4. |
Evaluation of \(\int\int_R f(x,y) \,dx \,dy \) in cartesian coordinate can be done using change of variables principle, among the choices given below which is correct explanation of change of variables principle? (Given let x=g(u,v) & y=h(u,v)) |
| A. | \(\int\int_S f(g(u,v),h(u,v)) \,du \,dv\) |
| B. | \(\int\int_S f(g(u,v),h(u,v)) \frac{d(x,y)}{d(u,v)} \,du \,dv\) |
| C. | \(\int\int_S f(g(u,v),h(u,v)) \frac{∂(x,y)}{∂(u,v)} \,du \,dv\) |
| D. | \(\int\int_S f(g(u,v),h(u,v)) \frac{∂(u,v)}{∂(x,y)} \,du \,dv\) |
| Answer» D. \(\int\int_S f(g(u,v),h(u,v)) \frac{∂(u,v)}{∂(x,y)} \,du \,dv\) | |