Question

Show that:
$integral subscript 1 superscript 5 open vertical bar straight x minus 3 close vertical bar space dx space equals space 4$

Solution

Let I = $integral subscript 1 superscript 5 open vertical bar straight x minus 3 close vertical bar space dx$
For $1 less or equal than straight x less or equal than 3 comma space space straight x minus 3 space less or equal than space 0 space space space space space space space space rightwards double arrow space space space space open vertical bar straight x minus 3 close vertical bar space equals space minus left parenthesis straight x minus 3 right parenthesis$
and for $3 less or equal than straight x less or equal than 5 comma space space space straight x minus 3 greater or equal than 0 space space space space space rightwards double arrow space space space open vertical bar straight x minus 3 close vertical bar space equals space straight x minus 3$
$therefore space space space space straight I space equals space integral subscript 1 superscript 3 open vertical bar straight x minus 3 close vertical bar dx space space plus integral subscript 3 superscript 5 open vertical bar straight x minus 3 close vertical bar space dx space equals space minus integral subscript 1 superscript 3 left parenthesis straight x minus 3 right parenthesis dx space plus integral subscript 3 superscript 5 left parenthesis straight x minus 3 right parenthesis space dx$
$equals negative open square brackets straight x squared over 2 minus 3 straight x close square brackets subscript 1 superscript 3 space plus space open square brackets straight x squared over 2 minus 3 straight x close square brackets subscript 3 superscript 5 equals space minus open square brackets open parentheses 9 over 2 minus 9 close parentheses space minus open parentheses 1 half minus 3 close parentheses close square brackets plus open square brackets open parentheses 25 over 2 minus 15 close parentheses minus open parentheses 9 over 2 minus 9 close parentheses close square brackets space equals space 9 over 2 minus 5 over 2 minus 5 over 2 plus 9 over 2 equals 4.$

For Daily Free Study Material Join wiredfaculty

Integrals

Show that:
$integral subscript 1 superscript 5 open vertical bar straight x minus 3 close vertical bar space dx space equals space 4$

Some More Questions From Integrals Chapter

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Phone Number

Email Address

Loaction