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Sketch the graph of y= |x+3 | and evaluate _{-6}^{0} |x+3 |dx

Question

Sketch the graph of $y = ∣ x + 3 ∣$ and evaluate $\int_{- 6}^{0} ∣ x + 3 ∣ d x$

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Sketch the graph of

y = ∣ x + 3 ∣

and evaluate

\int_{- 6}^{0} ∣ x + 3 ∣ d x

10 mins ago

Discuss this question LIVE

10 mins ago

Text solutionVerified

The given equation is

y = ∣ x + 3 ∣

Graph is plotted in the diagram.
It is known that,

(x + 3) \leq 0

for

- 6 \leq x \leq - 3

and

(x + 3) \geq 0

for

- 3 \leq x \leq 0

∴ \int_{- 6}^{0} ∣ (x + 3) ∣ d x = - \int_{- 6}^{- 3} (x + 3) d x + \int_{- 3}^{0} (x + 3) d x

= - [\frac{x ^{2}}{2} + 3 x]_{- 6}^{- 3} + [\frac{x ^{2}}{2} + 3 x]_{- 3}^{0}

= - [(\frac{( - 3 ) ^{2}}{2} + 3 (- 3)) - (\frac{( - 6 ) ^{2}}{2} + 3 (- 6))] + [0 - (\frac{( - 3 ) ^{2}}{2} + 3 (- 3))]

= - [- \frac{9}{2}] - [- \frac{9}{2}] = 9

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Question Text	Sketch the graph of $y = ∣ x + 3 ∣$ and evaluate $\int_{- 6}^{0} ∣ x + 3 ∣ d x$
Answer Type	Text solution:1
Upvotes	150