IIT JAM Follow
May 21, 2020 7:15 pm 50 pts
H Rule for Finding Definite Integral g To evaluate the definite integral f(x)dx (a < b) First find out the indefinite integral of f(x) i.e., f(x) dx, leaving the constant of integration c. X b ( Let f(x)dx = F(x) then, f(x) dx = F(x) xa =Lim F(x) - Lim F(x) X-b- X a To evaluate above the following cases may arise Case I: If f(x) is continuous at x = a and x = b Lim F(x) =F(a) Lim F(x) = F(b) x-b and X >at str (X) dx= F(b) -F(a) then Case l: If f(x) is continuous at x = a and discontinuous at x = b y= Lim F(x)=F(a) X-a+ f(x) dx =Lim F(x) -F(a) then Case ll: If fx) is discontinuous at x = a and continuous at x= b: Lim F(x) = F(b) Xb f(x) dx = F(b) - Lim F(x) then X-at
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