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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 , `isA. `pi//4`B. `pi(sqrt(2)+1)//4`C. `pi(sqrt(2)+1)//8`D. `(pi)/(8)` |
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Answer» Correct Answer - C `int_(0)^(pi//2)sin x dx =((pi)/(2)-0)/(4)[sin +sin ((pi)/(2))+2 sin((0+(pi)/(2))/(2))]` `=(pi)/(8)(1+sqrt(2))` |
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