Arc length of the curve y=7 from x=0 to x=1 is _____.

• A) 2
• B) -2
• C) 1
• D) -1

The volume of solid obtained when the region under the curve y = {x^3} over the interval [1,3] is revolved about the x-axis is

• A) V = \int\limits_1^3 {\pi {x^3}dy}
• B) V = \int\limits_1^3 {{x^6}dx}
• C) V = \int\limits_1^3 {\pi {x^3}dx}
• D) V = \int\limits_1^3 {\pi {x^6}dx}

Arc length of the curve y=x from x=0 to x=2 is _____.

• A) \int\limits_0^2 {\sqrt {1 + {{[\frac{d}{{dx}}(x)]}^2}} } dx
• B) \int\limits_0^2 {\sqrt {1 + {{[1]}^2}} } dx
• C) \int\limits_0^2 {\sqrt {1 + {{[\frac{{dy}}{{dx}}]}^2}} } dx
• D) All of the above

data:image/png;base64,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

• A) data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAASUAAAAZCAYAAAB3qDgVAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAAYDSURBVHhe7ZkLcRRbFEVjAQ1YwEMkoAELOMBBHKAABRjAAA7iYd5beVmpza7bPZ/Kg5lwVtUtuvuee/596IG7wzAMwxUxQ2kYhqtihtIwDFfFDKVhGK6KGUrDMFwVT0Pp69evh7u7u931/fv3/w78e438LfDly5cnfy/BnNwCnz59Orx///75bvhT/Pz58+V9uZXeeU3u7++f4v748ePzk8t4yhwvL0tocBpduM7BdQtDyYF0SXNkrMNwKvQLg8nrfKf+Fj58+HB4eHh4vruMl6GU9FAi0Q4ikv1aQ4mvr3MLxzQ+FQfTJTiY/hbOyeu1Q939sv9d0C+3/LV6ybu4gnfmx48fz3eXsXzreiglrzmUsHNOIs4dFDOUToNav5Wh5E+o3z2U6LVbHkrnvosrGEav8c5cPJTY55rlJyv07+qt5kgZljocBi7PO2Bc+ufvWFfaO2UotV7JoeRevrgdZzYkPvAMGZ73PrRd11Ye9sCv9M0hox+srYbr/GEXtuwbN7o9a2zZE1kH5NjLmLUj5omVvhqLttxT1gUZLwud6rVf9DHroX/K6lv6m/KN51zoA65Th7XVB1divBkL/mS/qX8P7OoX8p8/fz58+/btefdX1Ova6sGs6Qp+tmGL4aTtS37KLbsdhRax0UELh6yNQjDci0EZZJNnAfk8b0FNhvqk70lIFszzW1g44dq41e15m8RYsKOsDcOZfjHYy31Qt7psUmE/8891+pngB2eNW1357FgeOJN527JvHC5izWfGhy718af71lofjV/doD598Gy+EO1v6vZ8yiOb8WTd0z99AGTUCcilzSZ1gjq7bviRvmgfMl5t+Uw99lfG1zCA3r179yKDb5x5fHx8ul+B/oyX/Kfv6tizyz9wsxxEnjmX5QmcycQlGLH5gOQpqxO9Uj7pRHDfstkM7KFvBWfZUxaOJYW9rSS3rVWzA/c8Z+m7z7LJcx+/suAtTwzqzJX6kswRUI+838sbtPye/VUeuo4rfd1P6OBM5i+X8q0r0ReW9lf+tf3O/8o/+6nXFq0TkLfmoG/8mfBM/zveU/tQ/AmV+wwJ/gF6j64h9+k74NdWLYBBmHm0tueyPIFDXSTBSDqbBeXPDOwYnYjWDei02F0gYI9nFAvZTBq6t5JyrLjHmsGEa49rfXcvmy/3Wxd+GiNwveXXim6WzsMqb0nL79lf5Q35rGPr45pniWfwLWWb1gX6YM7S/sq/tt/5XvmHjqzfMVonoMOaAz6t9HJO+x1v124VX7Lyg68Xvp72yBxC+w741rrFYZhfY+hjUJ3LslMzSU07mwXFiW6gPVaJaLtZpC5Q7kHfozvlm44lOdYMfTbvV83X8vrmSlliyLwcA/m9PHQsTcvv2V+9FF3HlT6eJejAL3O1ReuCtpf3K//aPrKckZV/7Ge9jtE6wRjFWFtv+t/xdu1W8SWczfOrL6cV6QNwpnOyqoWsvsZa56ksuwFl7ZB0UrOgJiwdIRlbxdVpZFhct/5MaBYIWeyiQ7jOpKlvC86znwPBWI41A9fGyTPu9dv71Nv7W/kFbWsLsJX6km5EdOd9x9KkPHb27HceoJuv7XOd9pHdqxuYn9YFyLuvP9pP/3zG+dTBPksf2FOfcBaZzHnLJB0TcN6aC7ZSL35yLx1v126V/4Tz+MEXCzIMC+3xtbT170qcIQbOmDvOpf97dvka0y4r/TiXXzrVBOQyeSbDZRG8N5E4nXKZ4AbHW8ZkuDIJ6QPP2yf1meDc28IzriyIq/PCfcrgv7nInLD6LOdWeWbt5YH7FZzJ83m/yoP1TNIfWdnv2nYc5LLtA886z03uub/SBWmX58phA6yBOWu/ea4+ZVnoSdpn7K5IHaw+px+ScbGk4+0adL5X/vg/X/xs0i5fMDxjbwt9zhy0/XwXG84xALGLLPp6IGlj1YPJ9ts6/G9Q3FWBabJjBbtFaFgachhOYYbSH2Drb538W+otMUNpOIcZSn+A/jnheovs/TwahhUzlIZhuCpmKA3DcFXMUBqG4aqYoTQMw1UxQ2kYhqtihtIwDFfE4fAPmRCpGcfGPlwAAAAASUVORK5CYII=
• 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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

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) $\frac{{124\pi }}{5}$

The volume V of a cylinder with base area A and height h is calculated by ---------.

• A) V = A h^3
• B) V = A h
• C) V = 2A h
• D) V = A h^2

The volume of the solid generated by the region enclosed between $y = \sqrt x $ x=1 , x=4 and x-axis is revolved about y-axis.Which of the following equation gives the volume of solid by cylindrical shell ____.

• A) \[\frac{{114\pi }}{5}\]
• B) Both a and c
• C) 77.91
• D) \[\frac{{124\pi }}{5}\]

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

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

To Find the arc length, why might piecewise functions be more challenging than smooth functions?

• A) Piecewise functions have more complicated shapes.
• B) Piecewise functions have smoother curves.
• C) Piecewise functions are not defined on intervals.
• D) Piecewise functions may have discontinuities.

Distance between the points (-2,-3) and (-4,-1) using the distance formula is.........

• A) Sqrt(8)
• B) None of these
• C) Sqrt(10)
• D) 0

data:image/png;base64,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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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

The volume of the solid generated by the region enclosed between y = \sqrt x x=1 , x=3 and x-axis is resvolved by y-axis.Which of the following equation gives the volume of solid by cylindrical shell ____.

• A) V = \int\limits_1^3 {2\pi x\sqrt x dx}
• B) V = \int\limits_1^x {2\pi x\sqrt x dx}
• C) V = \int\limits_1^3 {2\pi {x^{\frac{3}{2}}}dx}
• D) Both b and c

Integral of (1-2x) from [0,1] is ……….

• A) 0
• B) 3
• C) 2
• D) 1

The volume of the solid generated by the region enclosed between y = \sqrt x x=1 , x=4 and x-axis is revolved about y-axis.Which of the following equation gives the volume of solid by cylindrical shell ____.

• A) \frac{{114\pi }}{5}
• B) \frac{{124\pi }}{5}
• C) 77.91
• D) Both a and c

If integral of ‘f(x)’ from [-1,2] = 4 and integral of ‘g(x)’ from [-1,2] = 8 ,then integral of (2f(x) +3g(x)) from [-1,2] =……..

• A) 38
• B) 36
• C) 32
• D) 30

Arc length of the curve y=10 from x=0 to x=2 is _____.

• A) 8
• B) 4
• C) $\sqrt[2]{2}$
• D) 2

The volume of the solid generated by the region enclosed between $y = \sqrt x $ x=1 , x=3 and x-axis is resvolved by y-axis.Which of the following equation gives the volume of solid by cylindrical shell ____.

• A) Both b and c
• B) $V = \int\limits_1^x {2\pi x\sqrt x dx} $
• C) $V = \int\limits_1^3 {2\pi x\sqrt x dx} $
• D) $V = \int\limits_1^3 {2\pi {x^{\frac{3}{2}}}dx} $

\[ Area\,\,between\,\,the\,\,x - axis\,\,and\,\,the\,\,curve\,\,y = \,\cos x;\,\,when\,\,0 \leqslant x \leqslant 2\pi \,\,is\, \]

• A) \[ \,4 \]
• B) \[ \,0\, \]
• C) \[ \,2 \]
• D) \[ None\,\,of\,\,these \]

Arc length of the smooth curve x=g(y) for y=a to y=b is…………………

• A) L = \int\limits_a^b {\sqrt {1 + (\frac{{dy}} {{dx}})^2 } } dx
• B) L = \int\limits_a^b {\sqrt {1 + (\frac{{dx}} {{dy}})^2 } } dy
• C)
• D)

data:image/png;base64,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

• A) data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAADUAAAAxCAYAAAB6d+FmAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAAGISURBVGhD7ZhRjYQwEEDPABKQgAQs4AALOEABCnCAAQxgAAM4QEQvr2EuzYX7YGGOTtOXNJuyP/u2M9MZvlyCZCkrZCkrZCkrZCkrZCkrZClhmiZX17UrisKvtm3dvu/Ht+9zWWoYBi+0bZvfL8vixbqu8/sYeCT8kBrH8di9zy0pTokT6vv+eBIHH0tJPlVV5XMsJm6dFMWBsEOOXIuFR3KKwtE0zbF7n0ekEDItxY8P7yUp6THl1WWpdV19xSvL8qdQxFTO4ZHwi40sZYUsZQVVKco+V4C0VGdLA1UpGl1GFD6l7M/z7K8BTS5Jnf3Tv9cZtFHcb8Adpz17qecUIRjK/kdXry6FgPSFhCKCMjVroS6FkIwl0idyepqDpaoURQEJySdOiJ6REJRnGqif1BvckiKMqGwxTb1wS4rSTHglI0VVY1gMC0EsfCRFkhN20gYlIRV2CElIhX0ciBR3UCxyl6Q4HQrDX8uk1BnJ5FQI+aXddV/llpTcUyzT7/0skKWskKCUc9838Hztp3BOowAAAABJRU5ErkJggg==
• 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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