Question

Evaluate the following integrals by expressing as a limit of sum.
(i) ${\int }_1^2(2x+5)dx$
(ii) ${\int }_1^2{x}^{2}dx$
(iii) ${\int }_1^2{e}^{x}dx$

Answer 1

$\left(i\right){\int }_1^2(2x+5)dx=[x^2+5x{]}_1^2\Rightarrow 4+10-(1+5)=8(ii){\int }_1^2{x}^{2}dx=[\frac{x^3}{3}{]}_1^2=\frac{8}{3}-\frac{1}{3}=\frac{7}{3}\left(iii\right){\int }_1^2{e}^{x}dx=[e^x{]}_1^2=e^2-e$