JEE Main 202313 Apr, Morning shiftMathematicsMediumIntegral Calculus369× since 2002Let 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) d tx∈R,S0(x)=x,Sk(x)=Ckx+k∫0xSk−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) d x, k=1,2,3, \ldotsC0=1,Ck=1−∫01Sk−1(x)dx,k=1,2,3,… Then S2(3)+6C3S_{2}(3)+6 C_{3}S2(3)+6C3 is equal to ____________.Your answerType your answer. Integers and decimals are accepted.CheckSkip · show solution
