To find: \(\int\limits_{1}^{3}
\)(2x2 + 5x)dx
Formula used:
where,
Here, f(x) = 2x2 + 5x and a = 1
Now, by putting x = 1 in f(x) we get,
f(1) = 2(1)2 + 5(1) = 2 + 5 = 7
f(1 + h) = 2(1 + h)2 + 5(1 + h)
= 2{h2 + 12 + 2(h)(1)} + 5 + 5h
= 2h2 + 4h + 2 + 5 + 5h
= 2h2 + 9h + 7
Similarly, f(1 + 2h)
= 2(1 + 2h)2 + 5(1 + 2h)
= 2{(2h)2 + 1 2 + 2(2h)(1)} + 5 + 10h
= 2(2h)2 + 2 + 8h + 5 + 10h
= 2(2h)2 + 18h + 7
= 2(2h)2 + 9(2h) + 7
{∵ (x + y)2 = x 2 + y 2 + 2xy}
Hence, the value of
