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Integrals

Question
CBSEENMA12032663
Wired Faculty App

The value of integral subscript negative straight pi over 2 end subscript superscript straight pi over 2 end superscript left parenthesis straight x cubed plus straight x space cosx space plus space tan to the power of 5 straight x plus 1 right parenthesis space dx space is

  • 0

  • 2

  • straight pi

  • 1

Solution

C.

straight pi

Let
        straight I space equals space integral subscript negative straight pi over 2 end subscript superscript straight pi over 2 end superscript space left parenthesis straight x cubed plus straight x space cosx space plus tan to the power of 5 straight x space plus space 1 right parenthesis dx
therefore space space space space space space space space equals space integral subscript negative straight pi over 2 end subscript superscript straight pi over 2 end superscript left parenthesis straight x cubed plus straight x space cosx plus tan to the power of 5 straight x right parenthesis space dx space plus space integral subscript straight pi over 2 end subscript superscript straight pi over 2 end superscript space 1 space dx space equals space 0 plus open square brackets straight x close square brackets subscript negative straight pi over 2 end subscript superscript straight pi over 2 end superscript open square brackets because space space straight x cubed plus straight x space cosx plus space tan to the power of 5 straight x space is space odd space function space and space so space integral subscript negative straight pi over 2 end subscript superscript bevelled straight pi over 2 end superscript left parenthesis straight x cubed plus straight x space cosx plus space tan to the power of 5 straight x right parenthesis space dx space equals space 0 close square brackets space space space space space space equals space straight pi over 2 minus open parentheses negative straight pi over 2 close parentheses space equals space straight pi over 2 plus straight pi over 2 space equals space straight pi
  therefore space space space space left parenthesis straight C right parenthesis space is space correct space answer.

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