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Mathematics : Integrals

Short Answer Type

121.

Evaluate: $integral subscript 0 superscript straight pi over 4 end superscript space fraction numerator sinx space cosx over denominator cos squared straight x plus sin to the power of 4 straight x end fraction dx.$

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122.

Evaluate the following definite integral:
$integral subscript 0 superscript straight pi over 4 end superscript fraction numerator sinx space cosx over denominator cos to the power of 4 straight x space plus space sin to the power of 4 straight x end fraction dx$

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123.

Evaluate the following definite integral:
$integral subscript straight pi over 6 end subscript superscript straight pi over 3 end superscript fraction numerator sinx plus cosx over denominator square root of sin space 2 straight x end root end fraction dx.$

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124.

Evaluate the following definite integral:
$integral subscript 0 superscript straight pi over 4 end superscript fraction numerator sinx plus cosx over denominator 9 plus 16 sin 2 straight x end fraction dx$

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125.

Evaluate the following definite integral:
$integral subscript 0 superscript straight pi over 2 end superscript sin space 2 straight x space tan to the power of negative 1 end exponent left parenthesis sin space straight x right parenthesis space dx.$

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126.

Prove that $integral subscript 0 superscript straight pi fraction numerator dx over denominator 5 plus 3 cosx end fraction space equals space straight pi over 4$

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127.

Evaluate $integral subscript 0 superscript straight pi fraction numerator dx over denominator 5 plus 4 space cosx end fraction.$

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128.

Evaluate the following:
$integral subscript 0 superscript straight pi over 2 end superscript fraction numerator dx over denominator 5 plus 4 space sinx end fraction$