Integral of x^2+x^3 is

NOTE: x^n means ‘x’ to the power ‘n’

• A) None of these
• B) (1/3)x^4+(1/4)x^3 +C
• C) (1/4)x^4+(1/3)x^3 +C
• D) x^3+x^4+C

Given a function f(x) = 1 / (x-1) and the interval is (0,2) ,then mean value theorem cannot be applied due to ……….

• A) Rational function
• B) None of these
• C) Discontinuity of the function in the given interval
• D) Open interval

$${\text{The integral }}\int {\sin (5x)dx} {\text{ will be equal to ?}}$$

• A) $$5\cos 5x + c$$
• B) $${\text{ - }}\frac{{\cos 5x}}{5} + c$$
• C) $$\frac{{\cos 5x}}{5} + c$$
• D) $${\text{ - }}\frac{{\cos 4x}}{5} + c$$

$$\text{The vertical asymptotes of the function }f(x)=\frac{{{x}^{2}}-2x+1}{x(x-2)}\text{ are}$$

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

3(12)+3(22)+3(32)+…+3(152) equals _____.

• A) 15(16)(17)/2
• B) 15(16)(30)/2
• C) 15(16)(31)/2
• D) 15(16)(29)/2

Mean value theorem states that between any two points A and B on a curve y=f(x) , there must be at least one point where the Tangent line to the curve is……………joining A and B

• A) Perpendicular to the secant line
• B) Parallel to the tangent line
• C) Perpendicular to the tangent line
• D) Parallel to the secant line

Why the equation: x^2 + 8 = 0 does not have approximate solution while using Newton's method?

• A) x^2 will always be nonnegative
• B) x^2 will always be negative
• C)
• D)

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

• 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) $$\sec (3{x^2}) + c$$