Integral Calculus Important Questions Paper

11th Standard

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Mathematics

All questions are compulsory.
Time : 01:00:00 Hrs
Total Marks : 50

    Part A

    10 x 1 = 10
  1. If \(\int {3^{1\over x}\over x^2}dx=k(3^{1\over x})+c\) ,then the value of k is

    (a)

    log 3

    (b)

    -log 3

    (c)

    \(-{1\over log3}\)

    (d)

    \({1\over log3}\)

  2. \(\int sin^3 \ xdx \) is

    (a)

    \({-3\over 4}cos \ x-{cos \ 3x\over 12}+c\)

    (b)

    \({3\over 4}cos \ x-{cos \ 3x\over 12}+c\)

    (c)

    \({-3\over 4}cos \ x+{cos \ 3x\over 12}+c\)

    (d)

    \({-3\over 4}sin \ x-{sin \ 3x\over 12}+c\)

  3. \(\int {dx\over e^x-1}\)is

    (a)

    \(log|e^x|-log|e^x-1|+c\)

    (b)

    \(log|e^x|+log|e^x-1|+c\)

    (c)

    \(log|e^x-1|-log|e^x|+c\)

    (d)

    \(log|e^x+1|-log|e^x|+c\)

  4. \(\int {sec^2x\over tan^2 \ x-1}\) dx

    (a)

    \(2log|{1-tan x\over 1+tan \ x}|+c\)

    (b)

    \(log|{1+tan x\over 1-tan \ x}|+c\)

    (c)

    \({1\over2}log|{tan x+1\over tan \ x-1}|+c\)

    (d)

    \({1\over2}log|{tan x-1\over tan \ x+1}|+c\)

  5. \(\int {1\over x\sqrt{(log \ x)^2+5}}dx\)is

    (a)

    \(log|x+\sqrt{x^2-5}|+c\)

    (b)

    \(log|logx+\sqrt{logx-5}|+c\)

    (c)

    \(log|logx+\sqrt{(logx)^2-5}|+c\)

    (d)

    \(log|logx-\sqrt{(logx)^2-5}|+c\)

  6. \(\int { \frac { 1 }{ 2 } } { sec }^{ 2 }\) x dx is _____ + c.

    (a)

    \(\frac { 1 }{ 2 } \) tan x

    (b)

    tan x

    (c)

    2 tan x

    (d)

    none of these

  7. \(\int { { 3 }^{ x+2 } } \) dx = __________+c.

    (a)

    \(\frac { { 3 }^{ x } }{ log3 } \)

    (b)

    \(9\left( \frac { { 3 }^{ x } }{ log3 } \right) \)

    (c)

    \(\frac { { 3 }^{ x } }{ 9log3 } \)

    (d)

    3x.9

  8. \(\int { \frac { \left( 1+logx \right) ^{ 2 } }{ x } } \) dx = _______+C.

    (a)

    \(\frac { \left( 1+logx \right) ^{ 3 } }{ 3 } \)

    (b)

    3 log ( 1 + log x)

    (c)

    2(1 + log x)

    (d)

    none of these

  9. \(\int { \frac { { e }^{ x } }{ \left( 1+{ e }^{ x } \right) ^{ 2 } } } \) dx =_______+c

    (a)

    \(\frac { 1 }{ 1+{ e }^{ x } } \)

    (b)

    -\(\frac { 1 }{ 1+{ e }^{ x } } \)

    (c)

    1 + ex

    (d)

    \(\frac { \left( 1+{ e }^{ x } \right) ^{ 3 } }{ 3 } \)

  10. \(\int { x } \) sin x dx = -x cos x + a, then a =  

    (a)

    sin x + c

    (b)

    cos x + c

    (c)

    c

    (d)

    none of these

  11. Part B

    5 x 2 = 10
  12. Integrate the following with respect to x.\(\sqrt{x}\)

  13. Integrate the following with respect to x: \({1\over sin ^2 x}\)

  14. Integrate the following with respect to x:9xe3x

  15. Evaluate \(\int { \sqrt { x } -{ cos }^{ 2 } } \frac { x }{ 2 } \)

  16. Evaluate \(\int { { x }^{ 2 } } \) log xdx

  17. Part C

    5 x 3 = 15
  18. Integrate the following with respect to x:\({x^{24}\over x^{25}}\)

  19. Integrate the following functions with respect to x:\({1\over 6-4x}\)

  20. Evaluate : \(\int (x-3)\sqrt{x+2}dx.\)

  21. Evaluate \(\int { \frac { { sin }^{ 6 }x+cos^{ 6 }x }{ sin^{ 2 }xcos^{ 2 }x } } \)

  22. Evaluate \(\int { \frac { 1 }{ { 4x }^{ 2 }-4x+3 } } \)dx

  23. Part D

    3 x 5 = 15
  24. Integrate the following with respect to x:\((1+x^2)^{-{1\over 2}}\)

  25. Evaluate \(\int { \frac { dx }{ tanx+cotx+secx+cosecx } } \)

  26. Evaluate \(\int { \frac { { e }^{ x }dx }{ { e }^{ 2x }+6{ e }^{ x }+5 } } \)

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