Integrals Test

Integrals

This is Integrals Test-05 for CBSE class 12 Maths.. There are 15 questions in this test with each question having around four answer choices.

Questions & Answers

1
The function\(f(x) = \int\limits_0^x {\log (t + \sqrt {1 + {t^2})} dt} \) is
  • A
    none of these
  • B
    a periodic function
  • C
    an odd function
  • D
    an even function
    Correct
2
\(\int\limits_{ - \pi /2}^{\pi /2} {\cos } \;\)t dt is equal to
  • A
    2
    Correct
  • B
    1
  • C
    – 1
  • D
    0
3
\(\int\limits_{ - 1}^1 {\left| {2x - 1} \right|} \)dx is equal to
  • A
    \(\frac{1}{2}\)
  • B
    \(\frac{5}{2}\)
    Correct
  • C
    \(\frac{{ - 1}}{2}\)
  • D
    – 2
4
\(\int\limits_0^{\pi /2} {\frac{1}{{1 + \tan x}}} dx\) is equal to
  • A
    none of these
  • B
    \(\pi \)
  • C
    \(\frac{\pi }{2}\)
    Correct
  • D
    \(\frac{\pi }{2}\)
5
\(\int\limits_0^{\pi /2} {\frac{1}{{1 + \sin x}}} dx\) is equal to
  • A
    \(\frac{1}{2}\)
  • B
    \(\frac{3}{2}\)
  • C
    0
  • D
    1
    Correct
6
\(\int\limits_0^{\pi /2} {\log \left| {\cos x} \right|} \)dx is equal to
  • A
    \( - \frac{\pi }{2}\log 2\)
    Correct
  • B
    \(\frac{\pi }{2}\log 2\)
  • C
    \(\pi \;log{\text{ }}2\)
  • D
    none of these.
7
\(\int\limits_2^2 {\left[ x \right]} \;dx\)is equal to
  • A
    0
  • B
    2
  • C
    – 2
    Correct
  • D
    none of these
8
\(\int\limits_{ - \pi /2}^{\pi /2} {{{\sin }^9}x\;dx} \) is equal to
  • A
    \(\frac{{2.8.4.2}}{{9.7.5.3}}\)
  • B
    0
    Correct
  • C
    \(\frac{{8.4.2}}{{9.7.5.3}}\)
  • D
    none of these
9
\(\int\limits_0^{\pi /2} {\log } \)(tan x) dx is equal to
  • A
    \(\int\limits_0^{\pi /2} {\log } \)(cot x ) dx
    Correct
  • B
    \( - \frac{\pi }{2}\log 2\)
  • C
    \(\frac{\pi }{2}\log 2\)
  • D
    none of these
10
\(\int\limits_0^{\pi /2} {\log } \)(cot x) dx is equal to
  • A
    none of these
  • B
    0
    Correct
  • C
    \(\frac{\pi }{2}\log 2\)
  • D
    \( - \frac{\pi }{2}\log 2\)
11
\(\int\limits_{ - 2}^2 {x\left| x \right|} dx\)is equal to
  • A
    \(\frac{8}{3}\)
  • B
    none of these
    Correct
  • C
    \(\frac{{ - 8}}{3}\)
  • D
    0
12
\(\int {\frac{{{{\tan }^{ - 1}}x}}{{1 + {x^2}}}dx} \;is\;equal\;to\)
  • A
    \(\log \left| {{{\tan }^{ - 1}}x} \right|\)
  • B
    none of these.
  • C
    \(\frac{1}{2}{({\tan ^{ - 1}}x)^2}\)
    Correct
  • D
    \((\log (1 + {x^2})){\tan ^{ - 1}}x\)
13
The value of the integral \(\int\limits_0^1 {{e^{{x^2}}}} \)dx is
  • A
    lies in [1, e]
    Correct
  • B
    less than 1
  • C
    none of these
  • D
    greater than e
14
\(\int\limits_0^2 {\sqrt {\frac{{2 + x}}{{2 - x}}} dx} \) is equal to
  • A
    none of these
    Correct
  • B
    \(\pi + 1\)
  • C
    \(\frac{\pi }{2} + 1\)
  • D
    \(\pi + \frac{3}{2}\)
15
\(\int {\tan x} {\sec ^2}\) x dx is not equal to
  • A
    \(\frac{{{{\sec }^2}x}}{2}\)
  • B
    none of these
    Correct
  • C
    \(\frac{{{{\tan }^2}x}}{2}\)
  • D
    \(\frac{1}{2}{(\cos x)^{ - 2}}\)