Question

$\int\limits^1_0 | 5x-3 | dx ,Evaluate the given integral expression:$

Answer 1

HELLO DEAR,




$\bold{\int\limits^1_0 | 5x-3 | dx}$


clearly, |5x - 3| = -(5x - 3( when <_ x <_ 3/5
(5x - 3) when 3/5 <_ x <_ 1 .

therefore, $\bold{\int\limits^1_0 |5x - 3|\,dx = \int\limits^{3/5}_0 |5x - 3|\,dx + \int\limits^1_{3/5}|5x - 3|\,dx}$

= $\bold{\int\limits^{3/5}_0-(5x - 3)\,dx + \int\limits^1_{3/5} {5x - 3}\,dx}$

= $\bold{\left[\begin{array}{cc}3x &-5x^2/2\end{array}\right]^{3/5}_0} + \bold{\left[\begin{array}{cc}5x^2/2 &-3x\end{array}\right]^1_{3/5}}$

= (9/5 - 9/10) + (-1/2 + 9/10) = 13/10.


I HOPE ITS HELP YOU DEAR,
THANKS