Evaluate the following integral as a limit of sums: ∫e^x dx, x ∈ [a, b]

Question

Evaluate the following integral as a limit of sums:

\(\int\limits_{a}^{b} \)e^x dx

Answer 1

To find: \(\int\limits_{a}^{b} \)e^xdx

Formula used:

where,

Now, by putting x = a in f(x) we get,

f(a) = e^a

f(a + h

 = (e)^a+h

= e^a+h

Similarly, f(a + 2h)

= e^a+2h

This is G.P.(Geometric Progression) of n terms whose first term(a) is 1

and common ratio(r)

Sum of n terms of a G.P. is given by,

Hence, the value of 

  \(\int\limits_{a}^{b} \)e^xdx = e^b -e^a