Question

Find $\stackrel{1}{\underset{0}{\int }}(2x+3)dx$ as the limit of a sum.

Answer 1

Let $I={\int }_0^1(2x+3)dx$

$=|{(x}^2+3x){|}_0^1$

$=(1^2-0^2)+3(1-0)$

$=1+3=4$

$⟹{\int }_0^1(2x+3)dx=4$