MCQ Bank
The\,\,area\,\,bounded\,\,by\,\,the\,\,curve\,\,y = \,4x - x^2 \,\,and\,\,x - axis\,\,is\,\,
- A) \frac{{30}} {7}\,\,
- B) \frac{{31}} {7}\,\,
- C) None\,\,of\,\,these
- D) \frac{{32}} {3}
If\,the\,curve\,\,over\,\,[a,\,b]\,is\,\,revolved\,about\,y - axis,\,then\,the\,volume\,is\,calculated\,by\,the\,formula\,\, - - - - - - -
- A) \int\limits_a^b {\pi \,[f(x)} ]^2 \,dx
- B) \int\limits_a^b {\pi \,[f(y)} ]^2 \,dy
- C)
- D)
By using cylindrical shells to find the volume of the solid when the region R in the first quadrant enclosed between y = x and y = {x^2} is revolved about the y-axis is ______.
- A) pi/6
- B) pi/3
- C)
- D)
If a function is constant over an interval, what can be said about its arc length on that interval?
- A) The arc length is proportional to the slope.
- B) The arc length is zero.
- C) The arc length is equal to the width of the interval.
- D) The arc length is infinite.
The volume of the solid generated by the region enclosed between y = \sqrt x x=0 , x=1 and x-axis is revolved about y-axis.Which of the following equation gives the volume of solid by cylindrical shell ____.
- A) \frac{{12\pi }}{5}
- B) None of the above
- C) \frac{{4\pi }}{5}
- D) \frac{{124\pi }}{5}
Find\,\,the\,\,area\,\,between\,\,y = x\,\,and\,\,y = \,\, - x(x - 4).
- A) 0
- B) \frac{7} {2}\,
- C) \frac{9} {2}\,
- D) None\,\,of\,\,these
Length of the arc y=c from x=0 to x=2 is ......
- A) 1
- B) 0
- C) 2
- D) None of these
A plane curve (not line) is a curve that lies in a ............ plane.
- A) None of these
- B) Two dimensional
- C) Three dimensional
- D) One dimensional
Arc length of the curve y=x from x=0 to x=1 is .........
- A) \sqrt 2
- B) 2\sqrt 2
- C) 0
- D) None of these.
If a function is continuous on a given interval then it is called....
- A) Discontinuous function.
- B) Smooth function.
- C) Piecewise function.
- D) Step function.
\[ \begin{gathered} If\,the\,curve\,\,y\, = \,f(x)\,\,over\,\,[a,\,b]\,is\,\,revolved\,about\,x - axis,\,then\,the\,volume\,is\,calculated\,by\,the\,formula\,\, - - - - - - - \ \end{gathered} \]
- A) \[ \int\limits_a^b {\pi \,[f(x)} ] \,dx \]
- B) \[ \int\limits_a^b {\pi \,[f(x)} ]^3 \,dx \]
- C) \[ \int\limits_a^b {\pi \,[f(x)} ]^4 \,dx \]
- D) \[ \int\limits_a^b {\pi \,[f(x)} ]^2 \,dx \]
Length of the curve y=3x from x=0 to x=1 is........
- A) Sqrt(10)
- B) Sqrt(5)
- C) 0
- D) None of these.
\begin{gathered} Find\,\,the\,\,area\,\,of\,\,the\,\,region\,\,to\,\,the\,\,left\,\,of\,the\,\,parabola\,\,x = 2y^2 ,\,\,to\,\,the\,\,right\,\,of\,\, \hfill \ the\,y - axis\,\,and\,\,between\,\,y = 1\,\,and\,\,y = 3 \hfill \\ \end{gathered}
- A) None\,\,of\,\,these
- B) \frac{{10}} {4}
- C) \frac{1} {3}
- D) \frac{{52}} {3}
If the function f(x) is not differentiable on the interval [a, b], what impact does it have on the calculation of the arc length?
- A) The arc length is approximated.
- B) The arc length is infinite.
- C) The arc length cannot be determined.
- D) The arc length is zero.
What happens to the arc length as the number of divisions of the interval increases?
- A) It becomes less accurate.
- B) It becomes more accurate.
- C) It decreases.
- D) It remains constant.
Find\,\,the\,\,area\,\,between\,\,y = x\,\,and\,\,y = \,\, - x(x - 4)
- A) None\,\,of\,\,these
- B) \frac{9} {2}\,
- C) 0
- D) \frac{7} {2}\,
The\,\,bounded\,\,region\,\,between\,\,the\,\,parabola\,\,y = 4x^2 \,\,and\,\,the\,\,line\,\,y = 6x - 2
- A) \frac{1} {6}\,
- B) None\,\,of\,\,these
- C) \frac{1} {{12}}
- D) \frac{1} {3}
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- B) data:image/png;base64,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
- C) data:image/png;base64,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
- D) data:image/png;base64,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
By using cylindrical shells to find the volume of the solid when the region R in the first quadrant enclosed between y=x and y = {x^2} is revolved about the y-axis is ______.
- A) V = \int\limits_0^1 {2\pi (x - {x^2})} dx
- B) V = \int\limits_0^1 {2\pi x(x - {x^2})} dx
- C) V = \int\limits_0^1 {\pi x(x - {x^2})} dx
- D) V = \int\limits_0^3 {2\pi x(x - {x^2})} dx
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- A) data:image/png;base64,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
- B) data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAADgAAAAjCAYAAADBl8lGAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAAF8SURBVFhH7ZUNjYYwDECxgAYs4AEJaMACDnCAAxSgAAMYwAEednkcTXoLHIOD8e2ylyxh4yd9a1cS88+JgqETBUMnCoZOFAydKBg6UTB0ouBdlGVpkiQ5HHfjTTDP8/XKL14Eh2EwVVWtM794Eazr2vR9v8784kWQ8pzneZ35xUmQ4JqmMVmWLY0gTdMlKy7wrn3+uq5b1qSxUL5PbYCTYFEUP4JAlsAI9Aie4XmBa+SmaVrm3Odb+pk7uVSiNA2CGsdxXfnGngMbs7WuQZhNfIJTgmSQZsE/TWdP1pBGXkNZH8EzriV/FmdByRqD3dYiUm4EiqhA5o5+D23bLu+9egY1yBD0VrbkPIkwwf92TnmfhnVUwn/h0hlktxHZagy6w5LpvcwgxX3ZjKe4JAh7gqwhSeD270FAzi5LXdp34iRoy3CtS1FD0AiSna3GwX3EdVlSqq92Ud0lGQRonz/N3hkFpOU7erwqeBYySxY/gUcEP4koGDpRMGyM+QIjHI7l/SdHzAAAAABJRU5ErkJggg==
- C) data:image/png;base64,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
- D) data:image/png;base64,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