Integral Calculus Model Question Paper

11th Standard

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Maths

Time : 02:00:00 Hrs
Total Marks : 60
    10 x 1 = 10
  1. If\(\int f(x)dx=g(x)+c\) ,then\(\int f(x)g'(x)dx\)

    (a)

    \(\int (f(x))^2dx\)

    (b)

    \(\int f(x)g(x)dx\)

    (c)

    \(\int f'(x)g(x)dx\)

    (d)

    \(\int (g(x))^2dx\)

  2. \(\int {e^{6logx}-e^{5logx}\over e^{4logx}-e^{3logx}}dx\) is

    (a)

    x+c

    (b)

    \({x^3\over 3}+c\)

    (c)

    \({3\over x^3}+c\)

    (d)

    \({1\over x^2}+c\)

  3. \(\int tan^{-1}\sqrt{1-cos \ 2x\over 1+cos \ 2x}dx\) is

    (a)

    x2+c

    (b)

    2x2+c

    (c)

    \({x^2\over2}+c\)

    (d)

    \(-{x^2\over2}+c\)

  4. \(\int {sin^8x-cos^8x\over 1-2sin^2 \ x \ cos^2 \ x}dx\) is

    (a)

    \({1\over2}sin 2x+c\)

    (b)

    \(-{1\over2}sin 2x+c\)

    (c)

    \({1\over2}cos 2x+c\)

    (d)

    \(-{1\over2}cos 2x+c\)

  5. \(\int{x^2+cos^2x\over x^2+1}cosec^2xdx\) is

    (a)

    cot x+sin -1x+c

    (b)

    -cot x+tan-1x+c

    (c)

    -tan x+cot-1x+c

    (d)

    -cot x-tan-1x+c

  6. \(\int \sqrt{{1-x\over 1+x}}dx\) is

    (a)

    \(\sqrt{1+x^2}+sin^{-1}x+c\)

    (b)

    \(sin^{-1}x-\sqrt{1+x^2}+c\)

    (c)

    \(log|x+\sqrt{1-x^2}|-\sqrt{1-x^2}+c\)

    (d)

    \(\sqrt{1-x^2}+log|x+\sqrt{1-x^2}|+c\)

  7. \(\int {dx\over e^x-1}\)is

    (a)

    \(log|e^x|-log|e^x-1|+c\)

    (b)

    \(log|e^x|+log|e^x-1|+c\)

    (c)

    \(log|e^x-1|-log|e^x|+c\)

    (d)

    \(log|e^x+1|-log|e^x|+c\)

  8. \(\int x^2e^{x\over2}dx\) is

    (a)

    \( x^2e^{x\over2}-4xe^{x\over2}-8e^{x\over2}+c\)

    (b)

    \( 2x^2e^{x\over2}-8xe^{x\over2}-16e^{x\over2}+c\)

    (c)

    \( 2x^2e^{x\over2}-8xe^{x\over2}+16e^{x\over2}+c\)

    (d)

    \( x^2{e^{x\over2}\over 2}-{xe^{x\over2}\over 4}+{e^{x\over2}\over 8}+c\)

  9. \(\int {x+2\over \sqrt{x^2+1}}dx\)is

    (a)

    \(\sqrt{x^2-1}-2 log|x+\sqrt{x^2-1}|+c\)

    (b)

    \(sin^{-1}x-2 log|x+\sqrt{x^2-1}|+c\)

    (c)

    \(2 log|x+\sqrt{x^2-1}|-sin^{-1}x+c\)

    (d)

    \(\sqrt{x^2-1}+2log|x+\sqrt{x^2-1}|+c\)

  10. \(\int e^{\sqrt{x}}dx\) is

    (a)

    \(2\sqrt{x}(1-e^{\sqrt{x}})+c\)

    (b)

    \(2\sqrt{x}(e^{\sqrt{x}}-1)+c\)

    (c)

    \(2e^{\sqrt{x}}(1-\sqrt{x})+c\)

    (d)

    \(2e^{\sqrt{x}}(\sqrt{x}-1)+c\)

  11. 10 x 2 = 20
  12. Integrate the following with respect to x. x10

  13. Integrate the following with respect to x. \({1\over cos^2 \ x}\)

  14. Integrate the following with respect to x:\({1\over 1+x^2}\)

  15. Integrate the following with respect to\({1\over (3x-2)}\)

  16. If f '(x)=4x-5 and f(2)=1, find f(x).

  17. Evaluate :\(\int e^{xlog2}e^x dx\)

  18. Integrate the following functions with respect to x :(2x−5)(36+4x)

  19. Integrate the following with respect to x eax cos bx

  20. Evaluate the following integrals \(\int{1\over (x+2)^2+1}dx\)

  21. \(\frac { cosx }{ { sin }^{ 2 }x } \)

  22. 5 x 3 = 15
  23. Integrate the following with respect to x: 123

  24. Integrate the following functions with respect to x: e3x-6

  25. Evaluate the following integrals:\({15\over \sqrt{5x-4}}-8cot (4x+2)cosec(4x+2)\)

  26. Evaluate :\(\int(tan \ x+cot \ x)^2dx\)
     

  27. Integrate the following functions with respect to x :\({1+cos \ 4x \over cot \ x-tan \ x}\)

  28. 3 x 5 = 15
  29. Integrate the following with respect to x:\((1+x^2)^{-1}\)

  30. A tree is growing so that, after t - years its height is increasing at a rate of \({18\over \sqrt{t}}\) cm per year Assume that when t = 0, the height is 5 cm. Find the height of the tree after 4 years

  31. Integrate the following functions with respect to x :\(x+1\over (x+2)(x+3)\)

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