The value of ∫−$$13$$ $${$$|x−$$2$$|$$+$$[x]$$}dx$$, where x denotes the greatest integer less than or equal to x is

Question

The value of  ∫−$$13$$ $${$$|x−$$2$$|$$+$$[x]$$}dx$$, where x denotes the greatest integer less than or equal to x is

Infinity Learn · Accepted Answer

∫−$$13$$ $${$$|x−$$2$$|$$+$$[x]$$}dx=$$∫−$$10$$ $${$$|x−$$2$$|$$+$$[x]$$}dx+$$ ∫$$01$$ $${$$|x−$$2$$|$$+$$[x]$$}dx+$$∫$$12$$ $${$$∣x−$$2$$∣$$+$$[x]$$}dx+$$∫$$23$$ $${$$|x−$$2$$|$$+$$[x]$$}dx=$$∫−$$10$$ (2$$−x−$$1)dx+$$∫$$01$$ $$(2$$−$$x+0)dx+$$∫$$12$$ $$(2$$−$$x+1)dx+$$∫$$23$$ $$(x$$−$$2+2)dx=x$$−$$x22$$−$$10+2x$$−$$x2201+3x$$−$$x2212+x2223=$$−−$$1$$−$$12+2$$−$$12+(6$$−$$2)−$$3$$−$$12+92$$−$$2=7$$

The value of $\int_{- 1}^{3} {| x - 2 | + [x]} d x$ , where $[x]$ denotes the greatest integer less than or equal to x is

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The value of ∫−13 {|x−2|+[x]}dx, where x denotes the greatest integer less than or equal to x is

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The value of $\int_{- 1}^{3} {| x - 2 | + [x]} d x$ , where $[x]$ denotes the greatest integer less than or equal to x is