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Applications of Integration 2 Mark Creative Question Paper With Answer Key

12th Standard

    Reg.No. :
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Maths

Time : 00:30:00 Hrs
Total Marks : 30

    2 Marks

    15 x 2 = 30
  1. Evaluate \(\int _{ 0 }^{ 1 }{ \left( \frac { { e }^{ 5logx }-{ e }^{ 4logx } }{ { e }^{ 3logx }-{ e }^{ 2logx } } \right) } \)

  2. Evaluate \(\int { \sum _{ r=0 }^{ \infty }{ \cfrac { { x }^{ r }{ 2 }^{ r } }{ r! } } dx } \)

  3. Evaluate \(\int { { e }^{ 3x }3^{ 2x }{ 5 }^{ x }dx } \)

  4. Evaluate \(\int _{ 0 }^{ \infty }{ \left( { a }^{ -x }-{ b }^{ -x } \right) } dx\)

  5. Find the slope of the tangent to the curve \(y=\int _{ 0 }^{ x }{ \frac { dt }{ 1+{ t }^{ 3 } } stx=1 } \) 

  6. Find the area bounded by the curve y=sin2x between the ordinates x=0.x=π and x-axis.

  7. Find the volume of the solid y=x3,x=0,y=1 is revolved about the y-axis.

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

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

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

  11. Find the area of the region enclosed by the curve \(y=\sqrt { x } +1\)  the axis of x and the lines x = 0 and x = 4.

  12. Find the volume of the solid obtained by revolving the area of the triangle whose sides are x = 4, y = 0 and 3x – 4y = 0 about x axis.

  13. Find the area of the region bounded by the curve \(\sqrt { x } +\sqrt { y } =\sqrt { a } \) (x,y>0) and the co-ordinate axes.

  14. Find the area of the region bounded by the curves y=2x.y=-2x-x2 and the lines x=0 and x=2

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

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