Integral Calculus – I Two Marks Questions

12th Standard EM

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Business Maths

Time : 00:45:00 Hrs
Total Marks : 30
    15 x 2 = 30
  1. Integrate the following with respect to x.

    \(\frac { 8x+13 }{ \sqrt { 4x+7 } } \)

  2.  Integrate the following with respect to x.

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

  3. Integrate the following with respect to x.
    \(\frac { { x }^{ 3 } }{ x+2 } \)

  4. \(If\quad f' \prime x=\frac { 1 }{ x } andf(1)=\frac { \pi }{ 4 } ,\quad then\quad findf(x)\)

  5. Integrate the following with respect to x.
    \(\frac { { e }^{ 3x }+{ e }^{ 5x } }{ { e }^{ x }+{ e }^{ -x } } \)

  6. If f ' (x) = ex and f (0)= 2, then find f (x)

  7. Integrate the following with respect to x.
    \(\frac { 1 }{ { sin }^{ 2 }x{ cos }^{ 2 }x } [Hint:si{ n }^{ 2 }+{ cos }^{ 2 }x=1]\quad \)

  8. Integrate the following with respect to x.
    \(\frac { { e }^{ 3logx } }{ { x }^{ 4 }+1 } \)

  9. Evaluate the following integrals:
    \(\frac { dx }{ { { 2-3x-2x }^{ 2 } } } \)

  10. Evaluate the following integrals:
    ഽ log(x −\(\sqrt { { x }^{ 2 }-1 } \)) dx

  11. Evaluate the following
    \(\int _{ 0 }^{ \infty }{ { e }^{ -4x } } { x }^{ 4 }dx\)

  12. Evaluate \(\int { { a }^{ 3{ log }_{ a }x } } dx\)

  13. Evaluate \(\int { \frac { { 2 }^{ x }+{ 3 }^{ x } }{ { 5 }^{ x } } dx } \)

  14. If f'(x) = 8x3 -2x2, f(2) = 1, find f(x)

  15. If \(\int _{ 0 }^{ a }{ { 3x }^{ 2 } } dx=8\) find the value of a

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