Integral Calculus Book Back Questions

11th Standard

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Maths

Time : 00:45:00 Hrs
Total Marks : 30
    5 x 1 = 5
  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. \(\int {e^x(1+x)\over cos^2(xe^x)}dx\) is

    (a)

    cot(xex)+c

    (b)

    sec(xex)+c

    (c)

    tan(xex)+c

    (d)

    cos(xex)+c

  3. \(\int {sec \ x\over \sqrt{cos 2x}}dx\) is

    (a)

    tan-1 (sin x)+c

    (b)

    2sin-1(tan x)+c

    (c)

    tan-1(cos x)+c

    (d)

    sin -1(tan x)+c

  4. \(\int{ {e^x}(x^2 \ tan^{-1}x+tan^{-1}x+1)\over x^2+1}dx\) is

    (a)

    ex tan-1(x+1)+c

    (b)

    tan-1(ex)+c

    (c)

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

    (d)

    ex tan-1 x+c

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

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

  6. 3 x 2 = 6
  7. Integrate the following with respect to x.\({sin \ x \over cos ^2 \ x}\)

  8. Integrate the following with respect to x: x11

  9. Integrate the following with respect to x:\({1\over \sqrt{1-25 x^2}}\)

  10. 3 x 3 = 9
  11. Integrate the following functions with respect to x: cos (5-11x)

  12. If f '(x)=3x2-4x+5 and f(1)=3, then find f(x).

  13. Evaluate :\(\int {3x+7\over x^2-3x+2}dx\)

  14. 2 x 5 = 10
  15. Integrate the following functions with respect to x:\({1\over \sqrt{1-81x^2}}\)

  16. Integrate the following functions with respect to x :\({8^{1+x}+4^{1-x}\over 2^x}\)

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