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