Search any question & find its solution
Question:
Answered & Verified by Expert
\( \int_{-5}^{5}|x+2| d x \) is equal to
Options:
Solution:
1540 Upvotes
Verified Answer
The correct answer is:
\( 29 \)
Given that, \( \int_{-5}^{5}|x+2| d x \)
\[
\begin{array}{l}
=\int_{-5}^{-2}|x+2| d x+\int_{-2}^{5}|x+2| d x \\
=-\int_{-5}^{-2}(x+2) d x+\int_{-2}^{5}(x+2) d x \\
=-\left[\frac{x^{2}}{2}+2 x\right]_{-5}^{-2}+\left[\frac{x^{2}}{2}+2 x\right]_{-2}^{5} \\
=-\left(\frac{4-25}{2}\right)-2(-2+5)+\frac{25-4}{2}+2(5+2) \\
=\frac{21}{2}+\frac{21}{2}-6 \pm 4=21+8=29
\end{array}
\]
\[
\begin{array}{l}
=\int_{-5}^{-2}|x+2| d x+\int_{-2}^{5}|x+2| d x \\
=-\int_{-5}^{-2}(x+2) d x+\int_{-2}^{5}(x+2) d x \\
=-\left[\frac{x^{2}}{2}+2 x\right]_{-5}^{-2}+\left[\frac{x^{2}}{2}+2 x\right]_{-2}^{5} \\
=-\left(\frac{4-25}{2}\right)-2(-2+5)+\frac{25-4}{2}+2(5+2) \\
=\frac{21}{2}+\frac{21}{2}-6 \pm 4=21+8=29
\end{array}
\]
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.