Important Questions of Integrals Mathematics | Zigya

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11.

Statement I - The value of the integral integral subscript straight pi divided by 6 end subscript superscript straight pi divided by 3 end superscript fraction numerator dx over denominator 1 plus space square root of tan space straight x end fraction is equal to π/6.
Statement II-integral subscript straight a superscript straight b straight f left parenthesis straight x right parenthesis space dx space equals space integral subscript straight a superscript straight b straight f left parenthesis straight a plus straight b minus straight x right parenthesis space dx

  • Statement -I is True; Statement -II is True; Statement-II is a correct explanation for Statement-I

  • Statement - I is True; Statement -II is true; Statement-II is not a correct explanation for Statement-I

  • Statement -I is True; Statement -II is False.

  • Statement -I is True; Statement -II is False.

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12.

If the integral integral fraction numerator 5 space tan space straight x over denominator tan space straight x minus 2 end fraction straight d space straight x space equals space straight x
space plus space straight a space log space vertical line space sin space straight x minus space 2 space cos space straight x vertical line space plus space straight k comma  then an equal to 

  • -1

  • -2

  • 1

  • 1

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13.

If g(x) = integral subscript 0 superscript straight x cos space 4 straight t space dt comma then g(x +π) equals

  • g(x)/g(π)

  • g(x) +g(π)

  • g (x) - g(π)

  • g (x) - g(π)

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14.

The value of integral subscript 0 superscript 1 fraction numerator 18 space log space left parenthesis 1 plus straight x right parenthesis over denominator 1 plus straight x squared end fraction space dx is

  • straight pi over 8 space log space 2
  • straight pi over 2 space log space 2
  • log 2

  • log 2

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15.

The integral  integral subscript straight pi over 4 end subscript superscript fraction numerator 3 straight pi over denominator 4 end fraction end superscript fraction numerator dx over denominator 1 plus space cos space straight x end fractionis equal to

  • -1

  • -2

  • 2

  • 2

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16. Let space straight I space space equals space integral subscript 0 superscript 1 space fraction numerator sin space straight x over denominator square root of straight x end fraction dx space and space straight J space equals space integral subscript 0 superscript 1 space fraction numerator cos space straight x over denominator square root of straight x end fraction space dx then which one is true?
  • I > 2/ 3 and J > 2

  • I < 2/ 3 and J < 2

  • I < 2/ 3 and J > 2

  • I < 2/ 3 and J > 2

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17.

The value of square root of 2 space integral fraction numerator sin space straight x space dx over denominator sin space open parentheses straight x minus begin display style straight pi over 4 end style close parentheses end fraction space is

  • space straight x plus space log open vertical bar cos space open parentheses straight x minus straight pi over 4 close parentheses close vertical bar space plus space straight C
  • straight x space minus log space open vertical bar sin space open parentheses straight x minus straight pi over 4 close parentheses close vertical bar space plus straight c
  • straight x space plus space log space open vertical bar sin space open parentheses straight x minus straight pi over 4 close parentheses close vertical bar space plus straight c
  • straight x space plus space log space open vertical bar sin space open parentheses straight x minus straight pi over 4 close parentheses close vertical bar space plus straight c
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18. let space straight F left parenthesis straight x right parenthesis space equals space straight f left parenthesis straight x right parenthesis space plus space straight f space open parentheses 1 over straight x close parentheses comma space where space straight f left parenthesis straight x right parenthesis space equals space integral subscript 1 superscript straight x fraction numerator log space straight t over denominator 1 plus straight t end fraction dt. Then F(e) equals
  • 1/2

  • 1

  • 2

  • 2

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19.

The value of the integral,integral subscript 3 superscript 6 fraction numerator square root of straight x over denominator square root of 9 minus straight x end root plus square root of straight x end fraction dx is

  • 1/2

  • 3/2

  • 2

  • 2

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20. integral subscript 0 superscript straight pi space xf space left parenthesis sin space straight x space right parenthesis space dx is equal to
  • straight pi integral subscript 0 superscript straight pi space straight f left parenthesis cos space straight x right parenthesis space dx
  • straight pi integral subscript 0 superscript straight pi space straight f left parenthesis sin space straight x right parenthesis space dx
  • straight pi over 2 integral subscript 0 superscript straight pi space straight f left parenthesis cos space straight x right parenthesis space dx
  • straight pi over 2 integral subscript 0 superscript straight pi space straight f left parenthesis cos space straight x right parenthesis space dx
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