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Let f be continuous and the function g i...

Let f be continuous and the function g is defined as `g(x)=int_0^x(t^2int_0^tf(u)du)dt` where `f(1) = 3`. then the value of `g' (1) +g''(1)` is

A

1

B

2

C

3

D

4

Text Solution

Verified by Experts

The correct Answer is:
C
`g(x)=int_(0)^(x)(t^(2).int_(1)^(t)f(u)du)dt`
`rArr" "g'(x)=x^(2)int_(1)^(x)f(u)du" hence "g'(1)=0`
`rArr" "g''(x)=x^(2)+(int_(1)^(x)f(u)du).2x`
`rArr" "g''(1)=f(1)+0=3`
`therefore" "g'(1)+g''(1)=3`
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