Ask Questions, Get Answers

Want to ask us a question? Click here
Browse Questions
Home  >>  CBSE XII  >>  Math  >>  Application of Integrals
0 votes

Sketch the graph of y=| x+3 | and evaluate$\Large \int\limits_{-6}^0\normalsize| x+3 |dx$

This question has appeared in model paper 2012

Can you answer this question?

1 Answer

0 votes
  • $\large\frac{d}{dx}$$(x^n)=nx^{n-1}$
Step 1:
$y=\mid x+3\mid=\left\{\begin{array}{1 1}-(x+3)\;for\; x<-3\\x+3\;for\; x\geq -3\end{array}\right.$
When $x<-3$
When x=-4,
When x=-5,
When x=-6,
Step 2:
When $x\geq -3$
$x=-1\Rightarrow y=2$
$x=-2\Rightarrow y=1$
$x=-3\Rightarrow y=0$
Step 3:
Required Area=Area of region ABC+Area of region OAD
$\qquad\qquad\quad=\int\limits_{-6}^{-3}\mid x+3\mid dx+\int \limits_{-3}^{0}\mid x+3\mid dx$
$\qquad\qquad\quad=\int\limits_{-6}^{-3}(-x-3)dx+\int \limits_{-3}^0(x+3)dx$
Step 4:
On applying limits we get,
answered Sep 10, 2013 by sreemathi.v

Related questions

Ask Question
student study plans
JEE MAIN, CBSE, NEET Mobile and Tablet App
The ultimate mobile app to help you crack your examinations
Get the Android App