InterviewSolution
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InterviewSolution
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योगफल की सिमा के रूप में `=int_(a)^(b) sin xdx` का मान ज्ञात कीजिएः। |
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Answer» यहाँ f(x)=sin x, nh=b-a हम जानते है की `underset(a)overset(b)int f(x)dx=underset(x to 0)limh[f(a)+f(a+h)+f(a+2h)+.....+f{a+(n-1)h}]` `underset(a)overset(b)int sinx dx` `=underset(h to 0)lim h[sin a+sin(a+h)+sin(a+2h)+....+sin{a+(n-1)h}]` `=underset(h to 0)lim h[(sin {a+((n-1)/(2))h}sin((nh)/(2))}/(sin((h)/(2)))]` `=underset(h to 0)lim h[(sin(a+(nh)/(2)-(h)/(2))sin((nh)/(2)))/(sin((h)/(2)))]` `=underset(h to 0)lim h[(sin(a+(b-a)/(2)-(h)/(2))sin((b-a)/(2)))/(sin ((h)/(2)))]` `=underset(h to 0)lim [((h)/(2))/(sin((h)/(2)))xx2xxsin(a+(b-a)/(2)(h)/2)]sin((b-a)/(2))]` `=1xx2xxsin(a+(b-a)/(2))sin((b-a)/(2))` `=2sin ((a+b)/(2))sin ((b-a)/(2))` `=cosa-cosb [therefore 2 sinA sin B=cos(A-B)-cos(A+B)` |
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