Evaluate the following integral: from Mathematics Integrals
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    Integrals

    Multiple Choice QuestionsShort Answer Type

    51.

    Explain the following integral:
    space integral subscript 0 superscript 1 fraction numerator 1 over denominator 1 plus straight x squared end fraction dx

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    Answer
    52.

    Explain the following integral:
    integral subscript 2 superscript 3 fraction numerator 1 over denominator straight x squared minus 1 end fraction dx

    89 Views
    Answer
    53.

    Explain the following integral:
    integral subscript 2 superscript 3 fraction numerator straight x over denominator straight x squared plus 1 end fraction dx

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    Answer
    54. Evaluate the following integral:
    integral subscript 1 superscript 2 fraction numerator dx over denominator left parenthesis straight x plus 1 right parenthesis space left parenthesis straight x plus 2 right parenthesis end fraction
    92 Views
    Answer
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    55. Evaluate the following integral:
    integral subscript 1 superscript 2 fraction numerator 5 straight x squared over denominator straight x squared plus 4 straight x plus 3 end fraction dx
    110 Views
    Answer
    56. Evaluate the following integral
    space integral subscript 2 superscript 3 fraction numerator 1 over denominator straight x squared minus 1 end fraction dx
    93 Views
    Answer
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    57. Evaluate the following integral:
    space space integral subscript 0 superscript 4 fraction numerator dx over denominator square root of straight x squared plus 2 straight x plus 3 end root end fraction

    Let I = space integral subscript 0 superscript 4 fraction numerator dx over denominator square root of straight x squared plus 2 straight x plus 3 end root end fraction space equals space integral subscript 0 superscript 4 fraction numerator 1 over denominator square root of left parenthesis straight x squared plus 2 straight x plus 1 right parenthesis plus 2 end root end fraction dx
           = integral subscript 0 superscript 4 fraction numerator 1 over denominator square root of left parenthesis straight x plus 1 right parenthesis squared plus left parenthesis square root of 2 right parenthesis squared end root end fraction dx space equals space open square brackets log space open vertical bar left parenthesis straight x plus 1 right parenthesis plus square root of straight x squared plus 2 straight x plus 3 end root close vertical bar close square brackets subscript 0 superscript 4
           equals space log left parenthesis 5 plus square root of 27 right parenthesis space minus space log left parenthesis 1 plus square root of 3 right parenthesis space equals space log open parentheses fraction numerator 5 plus 3 square root of 3 over denominator 1 plus square root of 3 end fraction close parentheses

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    58. Evaluate the following integral:
    integral subscript 4 superscript 9 fraction numerator square root of straight x over denominator open parentheses 30 minus straight x to the power of begin display style 3 over 2 end style end exponent close parentheses squared end fraction dx
    137 Views
    Answer
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    59.

    Evaluate the following definite integral
    integral subscript 0 superscript 2 fraction numerator 6 straight x plus 3 over denominator straight x squared plus 4 end fraction dx.

    94 Views
    Answer
    60.

    Evaluate the following definite integral
    integral subscript 0 superscript 1 fraction numerator 2 straight x over denominator 5 straight x squared plus 1 end fraction dx

    92 Views
    Answer
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