Evaluate -44-x-2- d x

F(x)=|x+2| = x+2 , amp; x≥ 2 (x+2) , amp; x lt; 2 nbsp; So, ∫_ 4^4|x+2|dx=∫_ 4^ 2 (x+2)dx+∫_ 2^4(x+2)dx =[ x^22 2x]_ 4^ 2+[x^22+2x]_ 2^4 = 2+4 ( 8+8 ...

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Byju's Answer

Standard XII

Mathematics

Rationalization Method to Remove Indeterminate Form

Evaluate ∫-44...

Question

Evaluate $4 \int - 4 | x + 2 | d x$

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Solution

$f (x) = | x + 2 |$
$= {\begin{matrix} x + 2, & x \geq - 2 - (x + 2), & x < - 2 \end{matrix}$

So,
$4 \int - 4 | x + 2 | d x = - 2 \int - 4 - (x + 2) d x + 4 \int - 2 (x + 2) d x$
$= {[- \frac{x^{2}}{2} - 2 x]}_{- 4}^{- 2} + {[\frac{x^{2}}{2} + 2 x]}_{- 2}^{4}$
$= - 2 + 4 - (- 8 + 8) + 8 + 8 - (2 - 4)$
$= 20$

Suggest Corrections

Evaluate 4∫−4|x+2| dx

f(x)=|x+2| ={x+2 ,x≥−2−(x+2) ,x<−2 So, 4∫−4|x+2|dx=−2∫−4−(x+2)dx+4∫−2(x+2)dx =[−x22−2x]−2−4+[x22+2x]4−2 =−2+4−(−8+8)+8+8−(2−4) =20

Evaluate $4 \int - 4 | x + 2 | d x$