+91-8076753736[email protected]
logo
logo
-->

Integrals

Question
CBSEENMA12032583
Wired Faculty App

By using the properties of definite integrals, evaluate the following integral:
integral subscript 0 superscript 2 straight pi end superscript cos to the power of 5 straight x space dx

Solution

Let I = integral subscript 0 superscript 2 straight pi end superscript cos to the power of 5 straight x space dx space equals space 2 integral subscript 0 superscript straight pi cos to the power of 5 straight x space dx
                                          open square brackets because space space cos to the power of 5 space left parenthesis 2 straight pi minus straight x right parenthesis space equals space cos to the power of 5 straight x and space integral subscript 0 superscript 2 straight a end superscript straight f left parenthesis straight x right parenthesis space dx space equals space 2 integral subscript 0 superscript straight a straight f left parenthesis straight x right parenthesis space dx space if space straight f left parenthesis 2 straight a minus straight x right parenthesis space equals space straight f left parenthesis straight x right parenthesis close square brackets equals space 0 space space space space space space space space space space space space space space space space space space space space space space space space space space space open square brackets table row cell because space cos to the power of 5 left parenthesis straight pi minus straight x right parenthesis space equals space left parenthesis negative cos to the power of 5 straight x right parenthesis space equals space minus cos to the power of 5 straight x end cell row cell and space integral subscript 0 superscript 2 straight a end superscript straight f left parenthesis straight x right parenthesis space dx space equals space 0 space if space straight f left parenthesis 2 straight a minus straight x right parenthesis space equals space minus straight f left parenthesis straight x right parenthesis end cell end table close square brackets space space space space space space space space space space space space space space space space space space space space space

Some More Questions From Integrals Chapter

Mock Test Series

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation