JEE Mains · Maths · STD 12 - 7.2 definite integral
Let for \(x \in R , S_0( x )= x\),\(S _{ k }( x )= C _{ k } x + k \int _0^{ x } S _{ k -1}(t) d t\), where \(C _0=1, C _{ k }=1-\int_0^1 S _{ k -1}( x ) dx , k =1,2,3 \ldots\). Then \(S _2(3)+6 C _3\) is equal to \(...........\).
- A \(17\)
- B \(16\)
- C \(18\)
- D \(11\)
Answer & Solution
Correct Answer
(C) \(18\)
Step-by-step Solution
Detailed explanation
\(S _{ k }( x )=C_k x + k \int_0^x S_{k-1}(t) d t\) Put \(k=2\) and \(x=3\) \(S _2(3)= C _2(3)+2 \int_0^3 S _1( t ) dt\) Also, \(S_1(x)=C_1(x)+\int_0^x S_0(t) d t\) \(=C_1 x+\frac{x^2}{2}\) \(S_2(3)=3 C_2+2 \int_0^3\left(C_1 t+\frac{t^2}{2}\right) d t\) \(=3 C_2+9 C_1+9\) Also,…
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