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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,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

Arc length of the curve $y = {x^{3/2}}$ on [1,3] is _____.

• A) $\int\limits_1^3 {\sqrt {1 + [\frac{d}{{dx}}\left( {{x^{3/2}}} \right)} ]} dx$
• B) $\int\limits_1^3 {\sqrt {1 + {{[\frac{d}{{dx}}\left( {{x^{3/2}}} \right)]}^2}} } dx$
• C)
• D)

If\,f(x)\, = \,\sqrt x ,\,\,then\,\,\int\limits_1^2 {\pi \,[f(x)} ]^2 \,dx\,\,is\,\, - - - - - - -

• A) \frac{3 \pi } {2}
• B) \frac{\pi } {2}
• C) \frac{5 \pi } {2}
• D) \frac{7 \pi } {2}

Let f is a smooth function on [0,3] what will be the arc length L of the curve y=f(x) from x=0 and x=3.

• A) \int\limits_0^3 {\sqrt {1 + {{[f(x)]}^2}} } dy
• B) \int\limits_0^3 {\sqrt {1 + {{[f'(x)]}^2}} } dx
• C) \int\limits_a^b {\sqrt {1 + {{[f'(x)]}^2}} } dy
• D) \int\limits_0^3 {\sqrt {1 + {{[f'(x)]}^2}} } dy

The volume of a cylindrical shell is given by ----------.

• A) (\pi {R^2} - \pi {r^2})h
• B) (\pi {R^2} + \pi {r^2})h
• C) \left( {\frac{{\pi {R^2}}}{{{r^2}}}} \right)h
• D) (\pi {R^2}{r^2})h

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)

The\,\,region\,\,bounded\,\,by\,\,the\,\,curves\,\,y = \sqrt x \,\,,\,\,y = 1\,\,and\,\,x = 4

• A) \,\,\frac{5} {3}
• B) None\,\,of\,\,these
• C) 0\,\,
• D) \frac{1} {2}

data:image/png;base64,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

• A) 10
• B) 8
• C) 12
• D) 14

What is the formula to calculate the surface area of a solid of revolution obtained by rotating a curve y=f(x) around the x-axis over the interval [a, b]?

• 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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

\[ Area\,\,between\,\,the\,\,curves\,\,y = 4 + 3x - x^2 \,\,and\,\,x - axis\,\,in\,\,sq.\,\,unit\,\,is\,\, \]

• A) \[ \frac{{125}} {3} \]
• B) \[ \frac{{125}} {4} \]
• C) \[ \frac{{125}} {6} \]
• D) \[ None\,\,of\,\,these \]

Distance between (3,-2) and (4,0) using the distance formula is…………….

• A) 0
• B) sqrt (5)
• C) None of these.
• D) sqrt (3)

\[ The\,\,region\,\,bounded\,\,by\,\,the\,\,curves\,\,y = \sqrt x \,\,,\,\,y = 1\,\,and\,\,x = 4 \]

• A) \[ None\,\,of\,\,these \]
• B) \[ 0\,\, \]
• C) \[ \frac{1} {2} \]
• D) \[ \,\,\frac{5} {3} \]

\[ The\,\,area\,\,bounded\,\,by\,\,the\,\,parabola\,\,y^2 \,\, = \,\,x\,,\,\,st.line\,\,y = 4\,\,and\,\,y - axis\,\,is \]

• A) \[ \frac{{64}} {3} \]
• B) \[ 7\sqrt 2 \, \]
• C) \[ None\,\,of\,\,these \]
• D) \[ \frac{{16}} {3} \]

{\text{Definite integral indicating the arc length of the curve }}y = x^2 {\text{ between }}x = 0{\text{ and }}x = 2{\text{ is }}.........

• A) L = \int\limits_0^2 {\sqrt {1 + 2x^2 } dx}
• B) L = \int\limits_0^2 {xdx}
• C) None of these.
• D) L = \int\limits_0^2 {\sqrt {1 + 4x^2 } dx}

\[ Area\,\,of\,\,the\,\,\,region\,\,bounded\,\,by\,\,the\,\,curves\,\,y = x^2 + 2\,\,,\,\,y = \,\, - x\,\,\,\,;\,\,x = 0\,\,and\,\,x = 1\,\,is \]

• A) \[ \frac{5} {{16}} \]
• B) \[ \frac{17} {{6}} \]
• C) \[ \frac{3} {{16}} \]
• D) \[ None\,\,of\,\,these \]

\[ If\,the\,curve\,\,over\,\,[a,\,b]\,is\,\,revolved\,about\,y - axis,\,then\,the\,volume\,is\,calculated\,by\,the\,formula\,\, - - - - - - - \]

• A) \[ \int\limits_a^b {\pi \,[f(y)} ]^2 \,dy \]
• B) \[ \int\limits_a^b {\pi \,[f(x)} ]^2 \,dx \]
• C)
• D)

{\text{The mean value theorem of }}f(x){\text{ at }}\left[ {x_k ,x_{k - 1} } \right]\,{\text{is }}........

• A) \frac{{f(x_k ) - f(x_{k - 1} )}} {{x_k - x_{k - 1} }} = f'(x^* _k )
• B) \frac{{f({x_k}) + f({x_{k - 1}})}}{{{x_k} + {x_{k - 1}}}} = f'({x_k})
• C)
• D)

\[ If\,f(x)\, = \,\sqrt x ,\,\,then\,\,\int\limits_1^2 {\pi \,[f(x)} ]^2 \,dx\,\,is\,\, - - - - - - - \]

• A) \[ \frac{7 \pi } {2} \]
• B) \[ \frac{3 \pi } {2} \]
• C) \[ \frac{5 \pi } {2} \]
• D) \[ \frac{\pi } {2} \]

When finding the surface area of a solid, what is the purpose of taking the limit of largest width on the x-axis approaches to 0?

• A) To simplify the calculations.
• B) It is not necessary for the surface area calculation.
• C) To obtain a more accurate approximation.
• D) To ensure convergence.

Arc length of the curve y = {x^{3/2}} on [1,3] is _____.

• A) \int\limits_1^3 {\sqrt {1 + {{[\frac{d}{{dx}}\left( {{x^{3/2}}} \right)]}^2}} } dx
• B) \int\limits_1^3 {\sqrt {1 + [\frac{d}{{dx}}\left( {{x^{3/2}}} \right)} ]} dx
• C)
• D)