Evaluate the following integrals as a limit of sums:
Formula used:
where,
Here, a = 0 and b = 1
Therefore,
Let,
Here, f(x) = 3x2 + 5x and a = 0
Now, by putting x = 0 in f(x) we get,
f(0) = 3(0)2 + 5(0) = 0 + 0 = 0
f(h)
= 3(h)2 + 5(h)
= 3h2 + 5h
Similarly, f(2h)
= 3(2h)2 + 5(2h)
= 3h2(2)2 + 5h(2)
Now take 3h2 and 5h common in remaining series
Put,
Since,