MCQ Bank
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- A) The area is dependent on the width of the interval [a, b].
- B) The area is infinite.
- C) The area is undefined.
- D) The area is zero.
How does the axis of rotation impact the choice between using the disk method or the washer method?
- A) It has no affect on the choice
- B) It determines the shape of the solid
- C) It determines the thickness of the cross-sections.
- D) It affects whether the solid has holes or voids along the axis.
$\frac{{{x^4}}}{4} - \frac{1}{4} = \_\_\_\_\_.$
- A) $\int\limits_1^x {{t^3}dt}$
- B) $\int\limits_1^x {{t^4}dt}$
- C)
- D)
Which of the following statements is true about $\int\limits_0^1 {(\sin x\cos x)dx}$?
- A) $$\int\limits_0^1 {(\sin x\cos x)dx} = \frac{1}{2}\int\limits_0^1 {\sin 2xdx}$$
- B) $$\int\limits_0^1 {(\sin x\cos x)dx} = \int\limits_0^1 {\sin xdx} + \int\limits_0^1 {\cos xdx}$$
- C) $$\int\limits_0^1 {(\sin x\cos x)dx} = 2\int\limits_0^1 {\sin xdx} \times 2\int\limits_0^1 {\cos xdx}$$
- D) $$\int\limits_0^1 {(\sin x\cos x)dx} = \int\limits_0^1 {\sin xdx} - \int\limits_0^1 {\cos xdx}$$
Use cylindrical shells to find the volume of the solid generated when the region ‘R’ enclosed between $$y = 2x + 1$$ and $$y = - 2x - 3$$ in the interval [1,3] is revolved about the y-axis is ______.
- A) $$V = \int\limits_1^3 {2\pi x\left( {(2x + 1) - ( - 2x - 3)} \right)} dx$$
- B) $$V = \int\limits_1^3 {2\pi x\left( {(2x + 1) + ( - 2x - 3)} \right)} dx$$
- C)
- D)
$$Area\,\,of\,\,the\,\,\,region\,\,bounded\,\,by\,\,the\,\,curves\,\,y = x^2 + 2\,\,,\,\,y = \,\, - x\,\,\,\,;\,\,x = 0\,\,and\,\,x = 1\,\,is$$
- A) $$\frac{3} {{16}}$$
- B) $$None\,\,of\,\,these$$
- C) $$\frac{17} {{6}}$$
- D) $$\frac{5} {{16}}$$
In general, an antiderivative of a product is the product of the antiderivatives.
- A) True
- B) False
- C)
- D)
$$Evaluate\;\frac{d} {{dx}}\int_2^x t dt$$
- A) $$x^3$$
- B) $$x$$
- C) $$x^2$$
- D) none of these
In order to fully determine the anti derivative of a function f (F(x)), we must have..........
- A) None of these
- B) Integration constant.
- C) Boundary conditions
- D) Initial conditions.
What could be the value of x if $\int\limits_0^x {3dx} > 15$ ?
- A) x>5
- B) x>3
- C) x>10
- D) x>15
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- C) data:image/png;base64,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.
- D) data:image/png;base64,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.
If f(x) =3x^2 then F(x) (antiderivative of f) will be
- A) 6x+c
- B) 6x
- C) x^3+2
- D) x^3+c
The integral of a constant function is 0.
- A) False
- B) True
- C)
- D)
$$\begin{gathered} If\,the\,curve\,\,y\, = \,f(x)\,\,over\,\,[a,\,b]\,is\,\,revolved\,about\,x - axis,\,then\,the\,volume\,is\,calculated\,by\,the\,formula\,\, - - - - - - - \ \end{gathered}$$
- A) $$\int\limits_a^b {\pi \,[f(x)} ]^2 \,dx$$
- B) $$\int\limits_a^b {\pi \,[f(x)} ]^3 \,dx$$
- C) $$\int\limits_a^b {\pi \,[f(x)} ]^4 \,dx$$
- D) $$\int\limits_a^b {\pi \,[f(x)} ] \,dx$$
In integration of $f(x)=x{{({{x}^{2}}+1)}^{3}}$ from x=0 to x=2 by substitution method, we take $u={{x}^{2}}+1$ then $du$= ................
- A) $$2xdx$$
- B) $$xdx$$
- C) $$dx$$
- D) 1
The conclusion of the 2nd fundamental theorem of calculus can be expressed in words as: "the derivative of an integral of a function is that…………..”
- A) none of these
- B) Previous function
- C) Next function
- D) Original function
If the definite integral of f(x)=2 over [x,2] is strictly less than ‘20’ then ----------
- A) x>20
- B) x>12
- C) x>18
- D) x>-8
First fundamental theorem of calculus gives the definite integral of a .......... function on a given closed interval in a quick way.
- A) Continuous
- B) Discontinuous
- C)
- D)
If the function and limits of definite integral are the same and variable of integration are changed, i.e $$\int_a^b {f(x)} dx = \int_a^b {f(t)} dt$$ Then the answer would be
- A) changed
- B) do not changed
- C)
- D)
........... gives a relation between definite integral and indefinite integral.
- A) None of these.
- B) Mean value theorem
- C) First fundamental theorem of Calculus
- D) Extreme value theorem