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

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

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

• A) 2ln2+2
• B) 2ln2-1
• C) ln2-1
• D) 2ln2+1

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) 1.5
• B) 0.5
• C) 2.5
• D) 1.05

Which of the following statements is true about [\sin x]_0^2 - [\tan x]_0^2?

• A) [\sin x]_0^2 - [\tan x]_0^2 = [2\sin x - 2\tan x]_0^2
• B) [\sin x]_0^2 - [\tan x]_0^2 = [\sin x - \tan x]_0^2
• C) [\sin x]_0^2 - [\tan x]_0^2 = [2\sin x + 2\tan x]_0^2
• D) None

What will be the value of \int\limits_0^2 {(\sin x + 3)dx} if \int\limits_0^2 {(10\sin x + 30)dx = 74} ?

• A) 7.4
• B) 4.2
• C) 5.4
• D) 3.6

\frac{{{x^4}}}{4} - \frac{1}{4} = \_\_\_\_\_.

• A) \int\limits_1^x {{t^3}dt}
• B) \int\limits_1^x {{t^4}dt}
• C)
• D)

\[ Evaluate\;\int_0^x {\cos t} dt = \]

• A) \[ {\cos t} \]
• B) \[ {\cos x} \]
• C) \[ \sin t \]
• D) \[ \sin x \]

The value of \int\limits_0^1 {{e^{ - x}}\,dx} \,\_\_\_\_\_\_.

• A) \frac{{1 - e}}{e}
• B) \frac{{1 + e}}{e}
• C) \frac{{e - 1}}{e}
• D) None of the above

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) \int\limits_0^1 {\sec x\tan xdx} = [\sec x]_0^1
• D) None

We can break up definite integrals across a sum or difference \int_a^b {f(x) \pm g(x)} dx = as

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

We can break up definite integrals across a sum or difference \[ \int_a^b {f(x) \pm g(x)} dx = \] as

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

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

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

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

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

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

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

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

• A) False
• B) True
• C)
• D)

The value of \int\limits_0^{\frac{\pi }{4}} {{{\tan }^2}x\,dx} \,\_\_\_\_\_\_.

• A) 0
• B) 1-\frac{\pi }{4}
• C) \frac{\pi }{4}-1
• D) None of the above

\int_a^b {f(x)} dx = 0 if__________.

• A) a = b
• B) a > b
• C) a < b
• D) None of these

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

• A) \int\limits_0^1 {(\sin x\cos x)dx} = \int\limits_0^1 {\sin xdx} + \int\limits_0^1 {\cos xdx}
• B) \int\limits_0^1 {(\sin x\cos x)dx} = \frac{1}{2}\int\limits_0^1 {\sin 2xdx}
• C) \int\limits_0^1 {(\sin x\cos x)dx} = \int\limits_0^1 {\sin xdx} - \int\limits_0^1 {\cos xdx}
• D) \int\limits_0^1 {(\sin x\cos x)dx} = 2\int\limits_0^1 {\sin xdx} \times 2\int\limits_0^1 {\cos xdx}

The value of\int\limits_{ - 2}^2 {|x|\,dx} \,\_\_\_\_\_\_.

• A) 0
• B) None of the above
• C) 4
• D) 2

Evaluate\;\frac{d} {{dx}}\int_1^x {t^2 } dt =

• A) x^2
• B) - x^2
• C) 3x^2
• D) none of these