Integral Calculus – I Book Back Questions

12th Standard EM

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Business Maths

Time : 00:45:00 Hrs
Total Marks : 30
    5 x 1 = 5
  1. \(\frac { 1 }{ { x }^{ 3 } } \)dx is

    (a)

    \(\frac { -3 }{ { x }^{ 2 } } +c\)

    (b)

    \(\frac { -1 }{ 2{ x }^{ 2 } } +c\)

    (c)

    \(\frac { -1 }{ { 3x }^{ 2 } } +c\)

    (d)

    \(\frac { -2 }{ { x }^{ 2 } } +c\)

  2. \(\frac{logx}{x}\)dx , x > 0 is

    (a)

    \(\frac12\)(log x)2 + c

    (b)

    -\(\frac12\)(log x)2

    (c)

    \(\frac { 2 }{ { x }^{ 2 } } +c\)

    (d)

    \(\frac { 2 }{ { x }^{ 2 } } +c\)

  3. \(\left[ \frac { 9 }{ x-3 } -\frac { 1 }{ x+1 } \right] \)dx is

    (a)

    \(log\left| x-3 \right|-log \left| x+1 \right| +c\)

    (b)

    \(log\left| x-3 \right|+log \left| x+1 \right| +c\)

    (c)

    \(9log\left| x-3 \right|-log \left| x+1 \right| +c\)

    (d)

    \(9log\left| x-3 \right|+log \left| x+1 \right| +c\)

  4. \(\int _{ 0 }^{ 1 }{ (2x+1) } dx\) is

    (a)

    1

    (b)

    2

    (c)

    3

    (d)

    4

  5. \(\int _{ -1 }^{ 1 }{ { x }^{ 3 }{ e }^{ { x }^{ 4 } } } \) dx is

    (a)

    1

    (b)

    2\(\int _{ -1 }^{ 1 }{ { x }^{ 3 }{ e }^{ { x }^{ 4 } } } \)dx

    (c)

    0

    (d)

    \({ e }^{ { x }^{ 4 } }\)

  6. 3 x 2 = 6
  7.  Integrate the following with respect to x.

    \(\frac { 1 }{ \sqrt { x+1 } +\sqrt { x-1 } } \)

  8. Integrate the following with respect to x.
    ex log a + ea log a − enlog x

  9. Integrate the following with respect to x.
    \(\sqrt { 1-sin2x } \)

  10. 3 x 3 = 9
  11. Evaluate \(\int { \frac { { 5+5e }^{ 2x } }{ { e }^{ x }+{ e }^{ -x } } dx } \)

  12. Evaluate \(\int _{ -1 }^{ 1 }{ ({ x }^{ 2 }+x)dx } \)

  13. Evaluate the integral as the limit of a sum: \(\int _{ 1 }^{ 2 }{ { x }^{ 2 } } \) dx

  14. 2 x 5 = 10
  15. Evaluate \(\int { { sin }^{ 2 }xdx } \)

  16. Evaluate
    \(\int _{ 0 }^{ \infty }{ { e }^{ -2x }{ x }^{ 5 }dx } \)
     

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