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Applications of Integration - Two Marks Study Materials

12th Standard EM

    Reg.No. :
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Maths

Time : 01:00:00 Hrs
Total Marks : 30
    15 x 2 = 30
  1. Evaluate \(\int _{ 0 }^{ x }{ { x }^{ 2 } } \)cos nxdx, where n is a positive integer.

  2. Evaluate the following:
    \(\int _{ 0 }^{ 1 }{ { x }^{ 3 }{ e }^{ -2x }dx } \)

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

  4. Evaluate the following
    \(\int _{ 0 }^{ \frac { \pi }{ 2 } }{ { sin }^{ 2 }x{ cos }^{ 4 }xdx } \)

  5. Evaluate the following
    \(\int _{ 0 }^{ 1 }{ { x }^{ 2 }{ (1-x) }^{ 3 }dx } \)

  6. Find, by integration, the volume of the solid generated by revolving about the y-axis, the region enclosed by x2 y =1+ and y = 3.

  7. Evaluate \(\int _{ 0 }^{ 1 }{ \frac { { e }^{ x } }{ 1+{ e }^{ 2x } } dx } \)

  8. Evaluate \(\int _{ 0 }^{ \frac { \pi }{ 2 } }{ { e }^{ 2x }cosxdx } \)

  9. Evaluate \(\int _{ 0 }^{ \frac { \pi }{ 2 } }{ { e }^{ -x } } \)

  10. Evaluate \(\int _{ 0 }^{ 1 }{ \left( \cfrac { { e }^{ 5logx }-{ e }^{ 4logx } }{ { e }^{ 3logx }-{ e }^{ 2logx } } \right) } \)

  11. If \(\int _{ 0 }^{ \infty }{ \cfrac { { x }^{ 2 }dx }{ \left( { x }^{ 2 }+{ a }^{ 2 } \right) \left( { x }^{ 2 }+{ b }^{ 2 } \right) \left( { x }^{ 2 }+{ c }^{ 2 } \right) } } =\cfrac { \pi }{ 2(a+b)(b+c)(c+a) } \) then find \(\int _{ 0 }^{ \infty }{ \cfrac { dx }{ \left( { x }^{ 2 }+4 \right) \left( { x }^{ 2 }+9 \right) } } \)

  12. Evaluate \(\int _{ 0 }^{ 1 }{ \cfrac { { e }^{ x } }{ 1+{ e }^{ 2x } } dx } \)

  13. Find the area bounded by y=x2+2,x-x-axis, x=1 and x=2

  14. Find the area enclosed between the parabola y2=4ax and the line x=a,x=9a.

  15. Find the area bounded by the curve y=cosax in one arc of the curve.

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