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If y={x}[x], then 3∫0y dx is equal to,where {.} and [.] are fractional part function and greatest integer function respectively. |
Answer» <p>If <span class="mjx-chtml" id="MathJax-Element-1-Frame"><span class="mjx-math" id="MJXc-Node-318619"><span class="mjx-mrow" id="MJXc-Node-318620"><span class="mjx-mi" id="MJXc-Node-318621"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.519em; padding-right: 0.006em;">y</span></span><span class="mjx-mo MJXc-space3" id="MJXc-Node-318622"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.077em; padding-bottom: 0.298em;">=</span></span><span class="mjx-mo MJXc-space3" id="MJXc-Node-318623"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">{</span></span><span class="mjx-mi" id="MJXc-Node-318624"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-msubsup" id="MJXc-Node-318625"><span class="mjx-base"><span class="mjx-mo" id="MJXc-Node-318626"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">}</span></span></span><span class="mjx-sup" style="font-size: 70.7%; vertical-align: 0.513em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-texatom" id="MJXc-Node-318627" style=""><span class="mjx-mrow" id="MJXc-Node-318628"><span class="mjx-mo" id="MJXc-Node-318629"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">[</span></span><span class="mjx-mi" id="MJXc-Node-318630"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mo" id="MJXc-Node-318631"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">]</span></span></span></span></span></span><span class="mjx-mo" id="MJXc-Node-318632"><span class="mjx-char MJXc-TeX-main-R" style="margin-top: -0.144em; padding-bottom: 0.519em;">,</span></span></span></span></span> then <span class="mjx-chtml" id="MathJax-Element-2-Frame"><span class="mjx-math" id="MJXc-Node-318633"><span class="mjx-mrow" id="MJXc-Node-318634"><span class="mjx-mstyle" id="MJXc-Node-318635"><span class="mjx-mrow" id="MJXc-Node-318636"><span class="mjx-munderover" id="MJXc-Node-318637"><span class="mjx-itable"><span class="mjx-row"><span class="mjx-cell"><span class="mjx-stack"><span class="mjx-over" style="font-size: 70.7%; padding-bottom: 0.236em; padding-top: 0.141em; padding-left: 0.81em;"><span class="mjx-texatom" id="MJXc-Node-318642" style=""><span class="mjx-mrow" id="MJXc-Node-318643"><span class="mjx-mn" id="MJXc-Node-318644"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">3</span></span></span></span></span><span class="mjx-op"><span class="mjx-mo" id="MJXc-Node-318638" style="vertical-align: 0.001em; padding-right: 0.388em;"><span class="mjx-char MJXc-TeX-size2-R" style="padding-top: 1.109em; padding-bottom: 1.109em;">∫</span></span></span></span></span></span><span class="mjx-row"><span class="mjx-under" style="font-size: 70.7%; padding-top: 0.236em; padding-bottom: 0.141em; padding-left: 0.025em;"><span class="mjx-texatom" id="MJXc-Node-318639" style=""><span class="mjx-mrow" id="MJXc-Node-318640"><span class="mjx-mn" id="MJXc-Node-318641"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">0</span></span></span></span></span></span></span></span><span class="mjx-mi MJXc-space1" id="MJXc-Node-318645"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.519em; padding-right: 0.006em;">y</span></span><span class="mjx-mtext" id="MJXc-Node-318646"><span class="mjx-char MJXc-TeX-main-R" style="margin-top: -0.291em; padding-bottom: 0.372em;"> </span></span><span class="mjx-mi" id="MJXc-Node-318647"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.003em;">d</span></span><span class="mjx-mi" id="MJXc-Node-318648"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span></span></span></span></span></span> is equal to,where {.} and [.] are fractional part function and greatest integer function respectively.</p><br><br> | |