Evaluate the following definite integral
$integral subscript 0 superscript straight pi over 4 end superscript space left parenthesis 2 sec squared straight x plus straight x cubed plus 2 right parenthesis dx$

Solution

Let I = $integral subscript 0 superscript straight pi over 4 end superscript space left parenthesis 2 sec squared straight x plus straight x cubed plus 2 right parenthesis space dx space equals space open square brackets 2 space tan space straight x plus straight x to the power of 4 over 4 plus 2 straight x close square brackets subscript 0 superscript straight pi over 4 end superscript$
= $open square brackets 2 space tan straight pi over 4 plus open parentheses begin display style straight pi over 4 end style close parentheses to the power of 4 over 4 plus 2 open parentheses straight pi over 4 close parentheses close square brackets space minus space left square bracket 2 space tan space 0 space plus space 0 space plus 0 right square bracket$
$equals space 2 cross times 1 plus straight pi to the power of 4 over 1024 plus straight pi over 2 minus left parenthesis 0 plus 0 plus 0 right parenthesis space equals space 2 plus straight pi to the power of 4 over 1024 plus straight pi over 2$

For Daily Free Study Material Join wiredfaculty

Integrals

Evaluate the following definite integral
$integral subscript 0 superscript straight pi over 4 end superscript space left parenthesis 2 sec squared straight x plus straight x cubed plus 2 right parenthesis dx$

Some More Questions From Integrals Chapter

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Phone Number

Email Address

Loaction