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Definite Integration question

2023 · 13 Apr · Shift 1 · Q42

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PYQ Library
JEE Main
Mathematics
Definite Integration
2023 · 13 Apr · Shift 1 · Q42

Definite Integration question

2023 · 13 Apr · Shift 1 · Q42

JEE MainMathematicsDefinite IntegrationNumerical+4 / −1

Let for

x \in \mathbb{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) d x, k=1,2,3, \ldots

Then

S_{2}(3)+6 C_{3}

is equal to

\underline{\hspace{2cm}}

.

Numerical answer

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