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  • Sketch the graph of y = |x+3| and evaluate integral |x+3| from -6 to 0.

Q : 4        Sketch the graph of  \small y=|x+3|  and evaluate   \small \int_{-6}^{0}|x+3|dx.

Answers (1)

best_answer

y=|x+3|

the given modulus function can be written as

x+3>0

x>-3

for x>-3

y=|x+3|=x+3

x+3<0

x<-3

For x<-3

y=|x+3|=-(x+3)

AOI graph

Integral to be evaluated is

\\\int_{-6}^{0}|x+3|dx\\ =\int_{-6}^{-3}(-x-3)dx+\int_{-3}^{0}(x+3)dx\\ =[-\frac{x^{2}}{2}-3x]_{-6}^{-3}+[\frac{x^{2}}{2}+3x]_{-3}^{0}\\ =(-\frac{9}{2}+9)-(-18+18)+0-(\frac{9}{2}-9)\\ =9

Posted by

Sayak

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