IIT JEE , AIEEE Forum - Mathematics , Integral Calculus

gau.rav

_{[0 ]}

^{[2 ]} e^xdx

Please evaluate as the limits of sum,Don't make by using direct methods.

chimanshu_007

nh = 2 here

_{[0 ]}

^{[2 ]} e^xdx = _{[h ]}

_{[ 0]} h [(f (a) + f(a+h) + f(a+2h) + .......... f(a + (n-1))h)]

solving we get

_{[h ]}

_{[ o]}h [ e⁰ + e^h + e^2h + .,..........+ e^(n-1)h]

_{[ h]}

_{[o ]}[ e^o { (e^nh - 1)/ (e^h - 1)} ],..........use sum of gp

multiply n divide by h here

_{[h ]}

_{[o ]}(h/h) [ (e² - 1) / ( e^h-1/h)]...................nh = 2

as

_{[h ]}

_{[ o]} e^h - 1 / h = 1

we get

e² - 1 / 1 = e² - 1

dats the answer