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Mathematics : Integrals

Short Answer Type

151.

By using the properties of definite integrals, evaluate the following integral:
$integral subscript 0 superscript straight pi over 2 end superscript fraction numerator square root of sinx over denominator square root of sinx plus square root of cosx end fraction dx$

90 Views

152.

Show that:
$integral subscript 0 superscript straight pi over 2 end superscript fraction numerator sin cubed straight x over denominator sin cubed straight x plus cos cubed straight x end fraction dx space equals space straight pi over 4$

106 Views

153.

Show that:
$integral subscript 0 superscript straight pi over 2 end superscript space fraction numerator sin to the power of 4 straight x over denominator sin to the power of 4 straight x plus cos to the power of 4 straight x end fraction dx space equals space straight pi over 4$

94 Views

154.

Show that:
$integral subscript 0 superscript straight pi over 2 end superscript fraction numerator cos to the power of 5 straight x over denominator sin to the power of 5 straight x plus cos to the power of 5 straight x end fraction dx space equals space straight pi over 4$

89 Views

155.

Evaluate:
$integral subscript 0 superscript straight pi over 2 end superscript fraction numerator sin to the power of begin display style 3 over 2 end style end exponent straight x over denominator sin to the power of begin display style 3 over 2 end style end exponent straight x plus cos to the power of begin display style 3 over 2 end style end exponent straight x end fraction dx space$

108 Views

156.

Evaluate:
$integral subscript 0 superscript straight pi over 2 end superscript fraction numerator sin to the power of begin display style 5 over 3 end style end exponent straight x over denominator sin to the power of begin display style 5 over 3 end style end exponent straight x plus cos to the power of begin display style 5 over 3 end style end exponent straight x end fraction dx space equals space straight pi over 4$

94 Views

157.

Evaluate:
$integral subscript 0 superscript straight pi over 2 end superscript fraction numerator square root of cotx over denominator square root of tanx plus square root of cotx end fraction dx space equals space straight pi over 4$

106 Views

158.

Show that:
$integral subscript 0 superscript straight pi over 2 end superscript fraction numerator dx over denominator 1 plus cot space straight x end fraction space equals space straight pi over 4$

94 Views

Long Answer Type

159.

Show that:
$integral subscript 0 superscript straight pi over 2 end superscript fraction numerator dx over denominator 1 plus square root of tan space straight x end root end fraction space equals space straight pi over 4$

78 Views

Short Answer Type

160.

Show that:
$integral subscript 0 superscript straight pi over 2 end superscript fraction numerator dx over denominator 1 plus square root of cot space straight x end root end fraction space equals space straight pi over 4$

81 Views