Integral Calculus Three Marks Questions

11th Standard

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Maths

Time : 00:45:00 Hrs
Total Marks : 30
    10 x 3 = 30
  1. Evaluate \(\int { \frac { { x }^{ 4 }+{ x }^{ 2 }+1 }{ { x }^{ 2 }+x-1 } } \)dx

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

  3. Evaluate \(\int { \frac { \left( { a }^{ x }+{ b }^{ x } \right) ^{ 2 } }{ { a }^{ x }{ b }^{ x } } } \)dx

  4. Evaluate if f'(x) = 3x2 - \(\frac { 2 }{ { x }^{ 3 } } \) and f (1) = 0, find f (x)

  5. Evaluate \(\int { \sqrt { 1+sinx } } \) dx, 0< x < \(\frac { \pi }{ 2 } \)

  6. Evaluate \(\int { \frac { sin }{ \sqrt { 3+2cosx } } dx } \)

  7. Evaluate \(\int { cot^{ 3 } } \) x dx

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

  9. Evaluate \(\int { \frac { { e }^{ -x } }{ 16+9{ e }^{ -2x } } } \)dx

  10. Evaluate \(\int { tan } ^{ -1 }\) x dx

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