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Applications of Integration Five Marks Questions

12th Standard EM

    Reg.No. :
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Maths

Time : 01:00:00 Hrs
Total Marks : 50
    10 x 5 = 50
  1. Evaluate\(\int _{ 0 }^{ 1 }{ x^3dx } \), as the limit of a sum.

  2. Evaluate\(\int _{ 1 }^{ 4 }{ ({ 2x }^{ 2 }-3) } \) dx, as the limit of a sum

  3. Evaluate \(\int _{ 0 }^{ x }{ { x }^{ 2 } } \)cos nxdx, where n is a positive integer.

  4. Evaluate: \(\\ \\ \int _{ -1 }^{ 1 }{ { e }^{ -\lambda x }(1-{ x }^{ 2 }) } dx\)

  5. Evaluate \(\int ^\frac {\pi}{2}_{0} \)( sin2 x + cos4 x ) dx

  6. Evaluate \(\int _{ 0 }^{ 1 }{ { x }^{ 5 }{ (1-{ x }^{ 2 }) }^{ 5 }dx } \)

  7. Evaluate \(\int _{ 0 }^{ 1 }{ { x }^{ 3 }{ (1-x) }^{ 4 }dx } \)

  8. Find the area of the region bounded between the parabola y2 ax = 4
    and its latus rectum

  9. Find the area of the region bounded between the parabolas y2 x = 4 and x2 y = 4.

  10. Using integration find the area of the region bounded by triangle ABC, whose vertices A, B, and C are (−1,1), (3, 2), and (0,5) respectively

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