∫2−1 (e3x+7x−5)dx
Here, a=−1, b=2, nh=2−(−1)=3
=limh→0 h[f(a)+f(a+h)+f(a+2h)+...+f(a+(¯¯¯¯¯¯¯¯¯¯¯¯¯n−1))h]
f(a)=f(−1)=e−3−7−5
f(a+h)=f(h−1)=e3(h−1)+7(h−1)−5
f(a+2h)=f(2h−1)=e3(2h−1)+7(2h−1)−5
f(a+¯¯¯¯¯¯¯¯¯¯¯¯¯n−1h)=f(¯¯¯¯¯¯¯¯¯¯¯¯¯n−1h−1)
=e3(¯¯¯¯¯¯¯¯¯n−1h−1)+7(¯¯¯¯¯¯¯¯¯¯¯¯¯n−1h−1)−5
=limh→0 h[(e−3−7−5)+(e3h.e−3+7h−7−5)+(e6h.e−3+14h−7−5)+...+e3(n−1)h.e−3+7(n−1) h−7−5]
=limh→0 h[e−3 (1+e3h+e2(3h)+...+e3(n−1)h)−7n−5n+7h+2(7h)+...+ (n−1) 7h]
=limh→0 h[e−3((e3h)n−1e3h−1)−7n−5n+7h((n−1)×n)2]
=limh→0 [e−3.e3nh−13×e3h−13h−7nh−5nh+72(nh−h)(nh)]
=[13e3×e9−11−7(3)−5(3)+72(3−0)(3)]
=e9−13e3−21−15+72×9
=e9−13e3+632−36
=e9−13e3+63−722
=e9−13e3−92