Question Number 79814 by Pratah last updated on 28/Jan/20
Commented by Pratah last updated on 28/Jan/20
$$\mathrm{yes}\:\mathrm{sir}\:\mathrm{thanks} \\ $$
Commented by mr W last updated on 28/Jan/20
$${correct}\:{sir}? \\ $$
Commented by mr W last updated on 28/Jan/20
$$\mathrm{1}+\mathrm{4}+\mathrm{9}+\mathrm{16}=\mathrm{30} \\ $$
Commented by abdomathmax last updated on 28/Jan/20
![∫_1 ^5 [x]^2 dx =Σ_(k=1) ^4 ∫_k ^(k+1) k^2 dx =Σ_(k=1) ^4 k^2 =1^2 +2^2 +3^2 +4^2 =1+4+9 +16 =14+16 =30](Q79870.png)
$$\int_{\mathrm{1}} ^{\mathrm{5}} \left[{x}\right]^{\mathrm{2}} {dx}\:=\sum_{{k}=\mathrm{1}} ^{\mathrm{4}} \:\int_{{k}} ^{{k}+\mathrm{1}} {k}^{\mathrm{2}} {dx}\:=\sum_{{k}=\mathrm{1}} ^{\mathrm{4}} \:{k}^{\mathrm{2}} \\ $$$$=\mathrm{1}^{\mathrm{2}} \:+\mathrm{2}^{\mathrm{2}} \:+\mathrm{3}^{\mathrm{2}} \:+\mathrm{4}^{\mathrm{2}} =\mathrm{1}+\mathrm{4}+\mathrm{9}\:+\mathrm{16}\:=\mathrm{14}+\mathrm{16}\:=\mathrm{30} \\ $$
Commented by Pratah last updated on 29/Jan/20
$$\mathrm{thanks}\:\mathrm{sir} \\ $$