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For every function f (x) which is twice ...

For every function f (x) which is twice differentiable , these will be good approximation of
`int_(a)^(b)f(x)dx=((b-a)/(2)){f(a)+f(b)}`, for more acutare results for ` cin(a,b),F( c) = (c-a)/(2)[f(a)-f( c)]+(b-c)/(2)[f(b)-f( c)]`
When ` c= (a+b)/(2)`
`int_(a)^(b)f(x)dx=(b-a)/(4){f(a)+f (b)+2 f ( c) }dx`
Good approximation of `int_(0)^(pi//2)sinx dx , `is

A

`pi//4`

B

`pi(sqrt(2)+1)//4`

C

`pi(sqrt(2)+1)//8`

D

`(pi)/(8)`

Text Solution

Verified by Experts

The correct Answer is:
C
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