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B
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C
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D
None of these
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Solution
The correct option is B
LetS=limπ→∞113+n3+423+n3+⋯+12n =limπ→∞113+n3+423+n3+⋯+n2n3+n3 ∴S=limπ→∞∑nr=1r2r3+n3=limπ→∞r2n3(r3n3+1) =limπ→∞∑nr=11n.(rn)2[1+(rn)3] Applying the formula, we get A=∫10x21+x3dx =13∫103x21+x3dx=13[loge(1+x3)]10=13loge2