MCQ Bank
The Volume of a cylindrical shell can be expressed as _______.
- A) V= (area of cross section).(thickness)
- B) V= (area of cross section).(height)
- C)
- D)
Antiderivative of f(x) =x is ............
- A) x^3
- B) (1/2) x^2+c
- C) x/2
- D) None of these.
$${\text{If }}f{\text{ is continuous at every point of }}[a,b]{\text{ and }}F{\text{ is anti - derivative of }}f{\text{ on }}[a,b]{\text{, then}}$$
- A) $$\int_a^b {f(x)} dx = F(a) - F(b)$$
- B) $$\int_a^b {f(x)} dx = F(a) + F(b)$$
- C) none of these
- D) $$\int_a^b {f(x)} dx = F(b) - F(a)$$
What does the definite integral $\int_a^b {f(x)} dx$ represent?
- A) The area under the curve $f(x)$ from $x = a$ to $x = b$
- B) The slope of the curve $f(x)$ from $x = a$ to $x = b$
- C) The maximum value of the function $f(x)$ from $x = a$ to $x = b$
- D) The derivative of the function $f(x)$ at the point $x = a$
$$The\,\,area\,\,bounded\,\,by\,\,the\,\,parabola\,\,y^2 \,\, = \,\,x\,,\,\,st.line\,\,y = 4\,\,and\,\,y - axis\,\,is$$
- A) $$\frac{{64}} {3}$$
- B) $$None\,\,of\,\,these$$
- C) $$\frac{{16}} {3}$$
- D) $$7\sqrt 2 \,$$
The value of $\int\limits_1^3 {\frac{1}{x}} dx = \_\_\_\_\_.$
- A) ln|3|-1
- B) Both a and c
- C) ln|3|+3
- D) ln|3|
If we change the letter for the variable of integration but don’t change the limits, then the values of the definite integral are unchanged.
- A) True
- B) False
- C)
- D)
What is the antiderivative of zero?
- A) Independent variable x
- B) Any constant
- C) Zero
- D) Dependent variable x
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- C) data:image/png;base64,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.
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What is the value of the antiderivatives $[\sin x]_0^1 - [\tan x]_0^1$?
- A) sin1 + tan1 +1
- B) None
- C) sin1 - tan1
- D) sin1 + tan1
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- A) data:image/png;base64,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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,iVBORw0KGgoAAAANSUhEUgAAANQAAAAVCAYAAAA+asAJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAAW/SURBVHhe7djbTSNBEIVhUiAGUiAHQiAGUiADMiADIiACEiABMuCBN3hA8uqzfKTaoj0Ma3PxMr/UYrqnum5d1R5xtNqRm5ub1enp6erx8XGzMo+7u7vVycnJ6v7+frMy5vb2dj0+g6urq9XZ2dlmtnCIXF9fv1tDX8lODaUpjo+PP9xMIU01tV+znp+fb2b7ZWmow+Ly8nJ9gYeHh4d1/Wmqn8JODaUYdw1Gwyjs72BpqO9Fc7hQXaxzcFbfVStz+eeGcjscHR2t/+6ChpTUbfQk5hDYdjtNJdingF83sobmrZ8HtaEcao/HjdjX7KEHflkvLi7WfpDjV25Qn6nW+q+vvfTC37p326dtfOO7/Z7tq7c1vBeP94bYq/3EW3Po73ufTHPtd739bMSX9/YbtZnI1/fJE6zVEd2e6RCn555DOup51Xrw/F7sH+VNQzGaQ+FcPaSaIMmzNsI7CamB0CFZnRxWPfiKfbGbJk7S+DY62MCego9uz9UHeukPXRdZa/VXmHzm9IkxDZecZN73xn9+J0fb9laSI7bFLp40crDPXAF5bx7/gnjJpJDIeG8+xRz71s3TIP6aJ59sJfbMq3zykfnobGstBDqzRxz8qjjDnIFYved/YhjV5C686QgHIhjOM5gD4hTnQy/GQNaeJFCiySWRHcmoSenUJNLRZSV8am+1G1uhxyDeHEgOXNyREZv90SnOeuCo/nlfC5quHGCe2Qn8qfMQv9kPWYt81R3iby4g+qs/sPZeUc2xX88p1PxGvlL3yKN8VbrOkQ066UaaMqRe+Diyj7p/H7y1sCHdHLpDNVnboMPY1kyI3m1B9SRKOnlFwL+pZCgAhWYPPXyZiqEeiH1uPIdhD10KsxefPdFj1FiyN0XHPr2gL/LW+Ri5Ts89et74WmMJ/E3+RmdmrevuzLEvb+Z9xF5yEXlzezKHZ/4kFu/jO6zVOapO2JMLRE7z6yvv1a866v5dGWYyN1s9YA6l2CAwhTBFCnkKwUwFNUoivxSyZNmbBFZyYGS8pz+2Ar3Vv8TtArCPDShKOsRjBPEb5OjO/hqL9+ykoGpOwZbckuNvf4/uN7IWWynCTuyjxwtr0R2dGZGdY78X/wj6yNnX5eXVmlzQKQ/kq0yfo/qA+pXh3HKGaajPZmhhdBOb118sjk45qFBSJFPkYBTjiJpENmtBg085+MoogeKqa/T2vbHH7xQ3m+yksZDPiXqYo4bis31pmkBnDjuQ6wWD5KiStdiiv59Z/InPo3itRTd5+jLyZRFblaz5Cw1d6wP1vMiJf9s59wZDvQxQayFUH+CZrvyNvZxXv7DoTJz74O8sbUjxcMYwr86BYyMHwUGORsaBSsRI1novhEpNYi9i/kh6P0ikeWpRiMFaiO0aVxqxFj9d5OwP9pAjD7HZU/1D5OyNLNIAyQk/yfQmA33Vb2QttuixXwGzaS4vNQ7xTjXUNubYT75rPsSXs4t/ZDL4lng9a0rwn+9ksh+Jp54XmfgQ2DV6XdhrJOd08yn68n4XhpmMM0mAQONEZXRj2Gs9TtpLx6hQIICuo9Jt0MMGnfzjZ01wRXGRM8jl0IN99FurhWmemzVYy4EHviRH9PSGD2xb736ykf1i2paHFG8la9VWLjLrBn+rTfq9r1jrujtz7efisS6umkPvrMmZPeapDX4b2euv9/3sq0zWuw9ITHRU5CJnYag9OsOnNFQKaluRVgQiSXNkR+QA/nX/oeAQezP+NsRfmyOMGuKQedNQbhBBzoW8rv5oU+S2qTfE/4hikc9+W/42NJM6qV86Pg93uZB/Im86Jz+JGmUuisYNNLc5JJKd0Wfk/0Q+v/rn429E09RPXOMjNXMozP8pWlhYeJeloRYW9sjSUAsLe2TdUK+vr6vn5+cfM15eXtY+LSwcGuuGUsRPT08/amiqhYWvwj9J9sGPbSg+LSx8FUtDLSzskf001Gr1Bw4u8c2YxX86AAAAAElFTkSuQmCC.
Which of the following statements is true about $\int\limits_0^1 {(\cos x + {{\sec }^2}x)dx}$?
- A) None
- B) $$\int\limits_0^1 {(\cos x + {{\sec }^2}x)dx} = [\sin x]_0^1 + [\tan x]_0^1$$
- C) $$\int\limits_0^1 {(\cos x + {{\sec }^2}x)dx} = [\sin x]_0^1 \times [\tan x]_0^1$$
- D) $$\int\limits_0^1 {(\cos x + {{\sec }^2}x)dx} = [\sin x]_0^1 - [\tan x]_0^1$$
What technique is commonly used to find the volume of 3D objects that do not have regular shapes?
- A) Extrusion.
- B) Projection.
- C) Slicing.
- D) Folding.
The volume of solid obtained when the region under the curve x=y over the interval [1,4] is revolved about the y-axis is
- A) $V = \int\limits_1^4 {\pi dx}$
- B) $V = \int\limits_1^4 {{y^2}dy}$
- C) $V = \int\limits_1^4 {\pi {y^2}dy}$
- D) $V = \int\limits_1^4 {\pi ydy}$
Which of the following is the value of definite integral of 5+5x , where the lower limit is -1 and upper limit is 1 ?
- A) 14
- B) 10
- C) 12
- D) 16
The Volume of a cylindrical shell is given by ______.
- A) V = (average radius).(height).(thickness)
- B) V = 2π (average radius).(height).(thickness)
- C)
- D)
The value of $\int\limits_0^1 {{e^{ - x}}\,dx} \,\_\_\_\_\_\_.$
- A) $\frac{{1 + e}}{e}$
- B) $\frac{{1 - e}}{e}$
- C) $\frac{{e - 1}}{e}$
- D) None of the above
What is the formula for the volume of a sphere?
- A) data:image/png;base64,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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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.
If integral of ‘f(x)’ from [3,4] = - 8 ,than integral of ‘f(x)’ from [4,3] is …………
- A) -8
- B) -9
- C) -6
- D) 8
If you increase the number of subintervals in the cylindrical shell method, what impact does it have on the accuracy of the volume approximation?
- A) Makes the method invalid.
- B) Decreases accuracy.
- C) No impact on accuracy.
- D) Increases accuracy.