$${\text{What}}\,{\text{does}}\,{\text{the}}\,{\text{indefinite}}\,{\text{integral }}\int_{}^{} {f(x)} dx\,{\text{represent?}}$$

• A) $${\text{Families}}\,{\text{of}}\,{\text{antiderivative}}\,{\text{of}}\,{\text{the}}\,{\text{function }}f(x)$$
• B) $${\text{Curvature}}\,{\text{of}}\,{\text{the}}\,{\text{curve}}$$
• C) $${\text{None}}\,{\text{of}}\,{\text{these}}$$
• D) $${\text{Area}}\,{\text{under}}\,{\text{the}}\,{\text{curve}}$$

The estimated area under f(x) = 12 / x
from x = 1 to x = 3 with left end points for
n = 2 is ________.

• A) 12.
• B) None of these.
• C) 18
• D) 10.

Integral of x^(-10) is

NOTE: x^n means ‘x’ to the power ‘n’

• A) - 1/(9x^9)+C
• B) None of these
• C) -10x^(-11)+C
• D) 1/(9x^9)+C

summation of (n+i) ; (i varies from 1 to 10 ) , here ‘i’ is known as the …….. of the summation.

• A) Upper limit
• B) Index
• C) None of these
• D) Lower limit

If $f$ is______________ on a closed interval $[a,b]$, then $f$, attains an absolute maximum value $f(c)$ and an absoulte minimum value $f(d)$ at some numbers $c$ and $d$ in $[a,b]$.

• A) None of these
• B) differentiable
• C) continuous
• D) constant

13+23+33+…+193 equals _____.

• A) [19(20)/2]2
• B) [19(20)]2/2
• C) 19(20)/22
• D) 19(20)2/2

x=1 is a critical value of the function.
f(x)=(x-1)^3

NOTE: x^n means ‘x’ to the power ‘n’

• A) False
• B) True
• C)
• D)

If the graph of $f$ lies above all of its tangents on an interval $I$, then it is called___________ on $I$.

• A) constant function
• B) concave downward
• C) concace upward
• D) None of these

Integral of x^101 is

NOTE: x^n means ‘x’ to the power ‘n’

• A) (1/102)x^102+C
• B) None of these
• C) 102x^102+C
• D) 101x^100 +C

To find the area between continuous curve f(x) and the closed interval [a,b] on x-axis, we take
-------------- of f(x) on the interval [a,b].

• A) left hand limit
• B) integral
• C) right hand limit
• D) derivative

What is the estimated area under f(x) = 10-x2 from x = 0 to x = 3 with left end points for n = 3?

• A) 15
• B) 21
• C) 25
• D) 30

Sigma notation is used to write lengthy……….in compact form.

• A) quotient
• B) sums
• C) difference
• D) products

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

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

If the closed interval [-2,2] is divided into ‘50’ equally spaced sub-intervals then the width of each sub-interval is ------------

• A) 2/25
• B) 1/25
• C) 4/25
• D) -4/25

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

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

An Inflection Point is a point where a curve changes from

• A) c. Both a and b
• B) d. None of these
• C) b. Concave down to concave up
• D) a. Concave up to concave down

$$\text{If a function }f\text{ has a relative extrema at }{{x}_{0}}\text{, then}$$

• A) $${f}'\left( {{x}_{0}} \right)>0$$
• B) $$\text{either}\,{f}'\left( {{x}_{0}} \right)=0\,\text{or }f\text{ is not differentiable at }{{x}_{0}}$$
• C) $$f\text{ is differentiable at }{{x}_{0}}$$
• D) $${f}'\left( {{x}_{0}} \right)\le 0$$

$$\text{If }{f}'(x)={{x}^{2}}-x\text{. Then the critical points of the function }f\text{ are}$$

• A) 0, 2
• B) 1, 2
• C) 1, -1
• D) 0, 1

If f(x) = Cos(x) + x, then which of the following is NOT true about it.

• A) Its anti – derivative is Sin(x) + x^2/2 + 6.
• B) Its anti – derivative is Sin(x) + x^2/2 + 4.
• C) Its anti – derivative is Sin(x) + x^2/2 + 10.
• D) Its anti – derivative is -Sin(x) + x^2/2 + 4.

$$\int {\tan x} dx = \_\_\_\_\_\_\_\_\_\_\_\_\_\_.$$

• A) $${\sec ^2}x + C$$
• B) $$\ln \left| {\sin x} \right| + C$$
• C) $$\ln |\cos x| + C$$
• D) $$\ln \left| {\sec x} \right| + C$$