JEE Mains · Maths · STD 12 - 7.2 definite integral
if \(\int_{- a }^{ a }(| x |+| x -2| d x =22,( a >2)\) and \([ x ]\) denotes the greatest integer \(\leq x ,\) then \(\int_{ a }^{- a }( x +[ x ]) d x\) is equal to ...........
- A \(2\)
- B \(3\)
- C \(4\)
- D \(5\)
Answer & Solution
Correct Answer
(B) \(3\)
Step-by-step Solution
Detailed explanation
\(\int_{-a}^{0}(-2 x+2) d x+\int_{0}^{2}(x+2-x) d x+\int_{2}^{a}(2 x-2) d x=22\) \(x^{2}-\left.2 x\right|_{0} ^{-a}+\left.2 x\right|_{0} ^{2}+x^{2}-\left.2 x\right|_{0} ^{a}=22\) \(a^{2}+2 a+4+a^{2}-2 a-(4-4)=22\) \(2 a^{2}=18 \Rightarrow a=3\)…
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