If “f” is a continuous function on [a,b] then \int\limits_a^b {f(x)\,dx = } \,\_\_\_\_\_\_.

• A) - \int\limits_b^a {f(x)\,dx}
• B) - \int\limits_c^a {f(x)\,dx}
• C) - \int\limits_a^b {f(x)\,dx}
• D) \int\limits_{b}^{b}{f(x)dx}

{\text{Which of the following is true for the definite integral }}\int_a^b {f(x)} dx =

• A) - \int_b^a {f(x)} dx
• B) \int_b^a {f(x)} dx
• C) \int_a^a {f(x)} dx
• D) - \int_a^b {f(x)} dx

What is the value of the antiderivatives [\sin x]_0^1 - [\tan x]_0^1?

• A) sin1 + tan1 +1
• B) None
• C) sin1 - tan1
• D) sin1 + tan1

The value of \int\limits_1^\infty {\frac{{dx}}{{{x^2}}}} \,\_\_\_\_\_.

• A) 1
• B) 0
• C) 3
• D) 4

\[ Evaluate\;\frac{d} {{dx}}\int_2^x t dt \]

• A) \[ x^2 \]
• B) \[ x^3 \]
• C) none of these
• D) \[ x \]

\int_a^b {f(x)} dx= _______________.

• A) f(a) + f(b)
• B) f(a) - f(b)
• C) - \int_b^a {f(x)} dx
• D) f(b) - f(a) + c

{\text{If }}f{\text{ is continuous at every point of }}[a,b]{\text{ and }}F{\text{ is anti - derivative of }}f{\text{ on }}[a,b]{\text{, then}}

• A) \int_a^b {f(x)} dx = F(b) - F(a)
• B) none of these
• C) \int_a^b {f(x)} dx = F(a) + F(b)
• D) \int_a^b {f(x)} dx = F(a) - F(b)

The value of \int\limits_0^{\frac{\pi }{6}} {\sin x\cos x\,dx} \,\_\_\_\_\_\_\_.

• A) \frac{1}{8}
• B) \frac{1}{4}
• C) 4
• D) 8

If the average value of y = sin3x with respect to x over [0, 2] is 0.525, then what will be the value of $\int\limits_0^2 {{{\sin }^3}xdx} $?

• A) 2.5
• B) 1.05
• C) 1.5
• D) 0.5

What could be the value of x if \int\limits_0^x {3dx} > 15 ?

• A) x>5
• B) x>15
• C) x>3
• D) x>10

The value of \int\limits_1^2 {dx = \_\_\_\_\_\_.}

• A) 1
• B) 2
• C) 0
• D) 3

Evaluate\;\int_0^x {\sin t} dt =

• A) 1 - \cos x
• B) 1 + \cos x
• C) 1 + \cos t
• D) 1 + \cos t

Which of the following statements is true about $\int\limits_0^1 {(\sin x - {{\sec }^2}x)dx} $?

• A) \[\int\limits_0^1 {(\sin x - {{\sec }^2}x)dx} = [\cos x]_0^1 - [\tan x]_0^1\]
• B) None
• C) \[\int\limits_0^1 {(\sin x - {{\sec }^2}x)dx} = - \,[\cos x]_0^1 - [\tan x]_0^1\]
• D) \[\int\limits_0^1 {(\sin x - {{\sec }^2}x)dx} = [\cos x]_0^1 + [\tan x]_0^1\]

$\int\limits_a^b {f(x)dx = \_\_\_\_\_\_.} $

• A) $ - \int\limits_b^a {f(x)dx} $
• B) $\int\limits_b^a {f(x)dx} $
• C)
• D)

In integration of f(x)=x{{({{x}^{2}}-3)}^{4}} from x=0 to x=2 by substitution method, we take u={{x}^{2}}-3 then du= ................

• A) dx
• B) x
• C) 2xdx
• D) 2x

The value of $\int\limits_1^x {{y^2}dy = \_\_\_\_\_.} $

• A) $\frac{{{y^3}}}{3} - \frac{1}{3}$
• B) $\frac{{{x^3}}}{3} - \frac{1}{3}$
• C)
• D)

If \[ \int_0^2 {(x^2 + 1)} dx = \frac{{14}} {3} \] Then the solution of \[ \int_2^0 {(x^2 + 1)} dx = \] will be....

• A) -14/3
• B) 14/3
• C) -3/14
• D) none of these

\[ \begin{gathered} {\text{If the upper and lower limits for the definite integral are the same, then }} \ \int_a^a {f(x)} dx = \\ \end{gathered} \]

• A) none of these
• B) negative integer
• C) zero
• D) positive integer

If “f” is a continuous function on [a,b] then \[\int\limits_a^b {f(x)\,dx = } \,\_\_\_\_\_\_.\]

• A) \[\int\limits_{b}^{b}{f(x)dx}\]
• B) \[ - \int\limits_a^b {f(x)\,dx} \]
• C) \[ - \int\limits_c^a {f(x)\,dx} \]
• D) \[ - \int\limits_b^a {f(x)\,dx} \]

For the adjacent intervals, [a,c] and [c,b],where c is any number,\[ \int_a^b {f(x)} dx = \]

• A) \[ \int_a^c {f(x)} dx + \int_c^b {f(x)} dx \]
• B) None of these
• C) \[ \int_a^b {f(x)} dx + \int_c^a {f(x)} dx \]
• D) \[ \int_a^c {f(x)} dx + \int_b^a {f(x)} dx \]