Evaluate the following integrals as a limit of sums:
Formula used:
where,
Here, a = 0 and b = 4
Therefore,
Let,
Here, f(x) = x + e2x and a = 0
Now, by putting x = 0 in f(x) we get,
f(0) = 0 + e2(0) = 0 + e0 = 0 + 1 = 1
f(h)
= h + (e)2h
= h + e2h
Similarly, f(2h)
= 2h + (e)2(2h)
= 2h + e4h
Take h common in some of the terms of series
Sum of n terms of a G.P. is given by,
and
Therefore,