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NVAMediumJEE Main 2023 · 13 April, Shift 1Definite Integrals

Mathematics Question from JEE Main 2023 · 13 April, Shift 1

Let for x∈R, S0(x)=x, Sk(x)=Ckx+k∫0xSk−1(t) dtx \in \mathbb{R}, \, S_0(x) = x, \, S_k(x) = C_k x + k \int_0^x S_{k-1}(t) \, dt where C0=1, Ck=1−∫01Sk−1(x) dx, k=1,2,3,…C_0 = 1, \, C_k = 1 - \int_0^1 S_{k-1}(x) \, dx, \, k = 1, 2, 3, \dots. Then S2(3)+6C3S_2(3) + 6C_3 is equal to:

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