If f(x) = * 20 c 4x + 3 ,, & if & 1 x 2 3x + 5 ,, & if & 2 < x 4 … - Vidyadip

MCQ

If $f(x) = \left\{ {\begin{array}{*{20}{c}}{4x + 3\,,}&{{\rm{if}}}&{1 \le x \le 2}\\{3x + 5\,,}&{{\rm{if}}}&{2 < x \le 4}\end{array}} \right.$ then $\int_1^4 {\,f(x)} \,dx = $

A
$80$
B
$20$
C
$ - 20$
✓
$37$

✓

Answer

Correct option: D.

$37$

d
(d) $\int_1^4 {f(x)dx = \int_1^2 {(4x + 3)dx + \int_2^4 {(3x + 5)\,dx} } } $

$ = \left| {2{x^2} + 3x} \right|_1^2 + \left| {\frac{{3{x^2}}}{2} + 5x} \right|_2^4 = 37$.

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