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) none of these
• C) -3/14
• D) 14/3

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

• A) \int\limits_b^a {f(x)dx}
• B) \int\limits_a^b {f(z)dz}
• C)
• D)

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

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

The value of \int\limits_1^{10} {3{x^2}\,dx} \,\_\_\_\_\_\_.

• A) 333
• B) 33
• C) 99
• D) 999

What will be the average value of y = cos3x with respect to x over [0, 2], if \int\limits_0^2 {{{\cos }^3}xdx} is equal to 0.66?

• A) 1.5
• B) 1.05
• C) 0.33
• D) 1.32

If\;\;m \leqslant f(x) \leqslant M\;for\;any\;two\;number\;such\;that\;,a \leqslant x \leqslant b,\;which\;of\;the\;following\;is\;true

• A) none of these
• B) m(b - a) \leqslant \int_a^b {f(x)} dx \leqslant M(b - a)
• C) m(b - a) \geqslant \int_a^b {f(x)} dx \leqslant M(b - a)
• D) m(b - a) \geqslant \int_a^b {f(x)} dx \geqslant M(b - a)

The expressions {{x}^{2}}+x,{{x}^{2}}+x+5,{{x}^{2}}+x-3 have the same .......

• A) Derivative
• B) Anti-derivative
• C)
• D)

In integration of f(x)=x{{({{x}^{2}}+1)}^{3}} from x=0 to x=2 by substitution method, we take u={{x}^{2}}+1 then du= ................

• A) 2xdx
• B) dx
• C) xdx
• D) 1

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

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

\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)

The value of \int\limits_1^3 {\frac{1}{x}} dx = \_\_\_\_\_.

• A) Both a and c
• B) ln|3|-1
• C) ln|3|
• D) ln|3|+3

What could be the value of x if \int\limits_x^0 {4dx} > 12 ?

• A) x< - 3
• B) x< - 4
• C) x<- 8
• D) x< - 5

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

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)