Which of the following will be left end points if the interval [-2,2] is divided into 4 equal subintervals.

• A) -1,0,1,2
• B) None of these
• C) -2,-1,1,2
• D) -2,-1,0,1

\[{\text{The integral }}\int {\frac{x}{{1 + {x^2}}}\,dx\,} {\text{will be equal to ?}}\]

• A) \[\frac{{\ln \left( {1 + {x^2}} \right)}}{2} + c\]
• B) \[2\ln (1 + {x^2}) + c\]
• C) \[{\text{ln(1 + }}{{\text{x}}^2}) + c\]
• D) \[\frac{{\ln \left( {1 - {x^2}} \right)}}{2} + c\]

\[{\text{The integral }}\int {\cot (2x)\,dx\,} {\text{will be equal to ?}}\]

• A) \[\frac{1}{2}\ln \left| {\sin (2x)} \right| + c\]
• B) \[\frac{1}{2}\ln \left| {\sec (2x)} \right| + c\]
• C) \[{\text{ln}}\left| {\sin (2x)} \right| + c\]
• D) \[\ln \left| {{\text{sec}}(2x)} \right| + c\]

$${\text{The integral }}\int {{{\left( {{x^3} + 1} \right)}^{10}}\,.3{x^2}\,dx\,} {\text{will be equal to ?}}$$

• A) $$- \frac{{{{\left( {{x^3} + 1} \right)}^{11}}}}{{11}} + c$$
• B) $$\frac{{{{\left( {{x^3} - 1} \right)}^{11}}}}{{11}} + c$$
• C) $${\text{None of these}}$$
• D) $$\frac{{{{\left( {{x^3} + 1} \right)}^{11}}}}{{11}} + c$$

\[{\text{The integral }}\int {\sec (x).\tan (x)\,dx\,} {\text{will be equal to ?}}\]

• A) \[\cos ec(x) + c\]
• B) \[\sec (x) + c\]
• C) \[{\text{None of these}}\]
• D) \[ - \ln \left| {\cos (x)} \right| + c\]

\[{\text{The integral }}\int {\cos e{c^2}(3{x^2})\,.6x\,dx\,} {\text{will be equal to ?}}\]

• A) \[ - \cot (3{x^2}) + c\]
• B) \[\sec (3{x^2}) + c\]
• C) \[{\text{cot(3}}{{\text{x}}^2}) + c,\]
• D) \[{\text{None of these}}\]

If integral of ‘f(x)’ from [1,2] = 5 ,and integral of ‘f(x)’ from [3,2] = 4 , than integral of ‘f(x)’ from [1,3] is ……….

• A) 1
• B) 2
• C) 9
• D) 3

The value of the definite integral of a function f(x)= x2 taken from [-7, 7] is 0.

• A) True
• B) False
• C)
• D)

If the value of definite integral of a function
f(x) taken from 1 to 3 is 2 and that of taken from 3 to 5 is 1 then value of definite integral taken from 1 to 5 is

• A) 3
• B) 1
• C) 0
• D) None of these

How can the volume of the solid formed by revolving a region R bounded by the graph of f(x) around the y-axis be approximated using cylindrical shells?

• 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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.

Antiderivative of cosx is ..........

• A) None of these.
• B) sinx+c
• C) cosx+sinx
• D) xsinx

$$The\,\,area\,\,bounded\,\,by\,\,the\,\,curve\,\,y = \,4x - x^2 \,\,and\,\,x - axis\,\,is\,\,$$

• A) $$\frac{{30}} {7}\,\,$$
• B) $$\frac{{32}} {3}$$
• C) $$None\,\,of\,\,these$$
• D) $$\frac{{31}} {7}\,\,$$

If the solid is revolved around the x-axis and generates a solid with a circular cross section of radius f(x) at x. Then the area of this cross section is

• A) $\pi r{\left[ {f(x)} \right]^3}$
• B) $\pi {\left[ {f(x)} \right]^2}$
• C) ${\left[ {f(x)} \right]^2}$
• D) $\pi \left[ {f(x)} \right]$

In general, an antiderivative of a product is the product of the antiderivatives.

• A) False
• B) True
• C)
• D)

We will get a _________ by moving a 2d plane in a direction along a line perpendicular to the region.

• A) Sphere
• B) Right cylinder
• C) Washer
• D) Cone

The method of slicing by integration is used for finding ----------

• A) surface
• B) length
• C) volume
• D) area

The volume of a cylindrical shell with an outer cylinder radius R=3, inner cylinder radius r=2, and length h=2 is……..

• A) data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACoAAAAbCAYAAAAK5R1TAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAAD5SURBVFhH7ZNdDYQwEAbPABKQgAQs4AALOEABCnCAAQxgAAM4QMRepte99H564WE5AukkhHbhYb529yYnIYlak0StSaLWXFO0aRq/+j9R0a7rJMuyj+cofopWVeV3x3N90XmepSiKr+3BYx0yKjoMg+R5/pThPY6j+7auq7Rt695lWTppoLbXwEVFQxBCAOFlWXz1USeMQhgC7sEmUUAK0b7vfUXcCesVE+A9iCWbRVUkFOWU6WXgJDnRvYiKIhX2JFJcM2utsZ+mye11+OjXMIwVUdG6rl+mmr0ODTA4YX8Siv+Q1TCWbL76o0mi1iRRa5KoNScRFbkDKiUX6vIFfNsAAAAASUVORK5CYII=.
• B) data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABwAAAAVCAYAAABVAo5cAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAACpSURBVEhL7ZJRDQMhEERrAAknAQlYwAEWcIACFOAAAxhABw4Qsc1srvzc8dGwbZqGl5AchPAys/egL7OF4myhOL8hDCGQUmq6aq3nzfe5CFNK/GAphZxzfNZ7Z1FrjfcrTCtFSshBzpm01vy9ylRojBnVee95SXArRHWo8AXSIaUEt8IYI1lrzx2NHwU1Y54rXIRIdxzHmB9AvTiTSDmd4afYQnH+XUj0BNGx4soTqKjgAAAAAElFTkSuQmCC.
• C) data:image/png;base64,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.
• D) data:image/png;base64,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.

Which of the following statements is true?

• A) An antiderivative of a sum is the sum of the twice of antiderivatives.
• B) A constant factor can be moved through an integral sign.
• C) None
• D) An antiderivative of a difference is k-times the difference of the antiderivatives.

The integral of f(x)=sin(2x) from x=0 to x=pi is ........

• A) None of thes.
• B) 1
• C) 2
• D) 0

Which of the following statements is true about $\int\limits_0^1 {\sec x\tan xdx}$?

• A) $$\int\limits_0^1 {\sec x\tan xdx} = [\sec x]_0^1 \times [\tan x]_0^1$$
• B) $$\int\limits_0^1 {\sec x\tan xdx} = [\sec x]_0^1 + [\tan x]_0^1$$
• C) None
• D) $$\int\limits_0^1 {\sec x\tan xdx} = [\sec x]_0^1$$