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Suppose we define the definite integral ...

Suppose we define the definite integral using the following formula `int_a^b f(x)dx=(b-a)/2 (f(x)+f(b))`, for more accurate result for `c in (a,b), F(c)=(c-a)/2 (f(a)+f(c))+(b-c)/2(f(b)+f(c))` and when `c=(a+b)/2, int_a^b f(x)dx=(b-a)/4(f(a)+f(b)+2f(c))` `int_0^pi sinxdx`= (A) `pi/8(1+sqrt(2))` (B) `pi/4(1+sqrt(2))` (C) `pi/(8sqrt(2))` (D) `pi/(4(sqrt(2))`

A

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

B

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

C

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

D

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

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