Question

please solve with solution ​

Answer 1

Step-by-step explanation:

We have,

$\int \limits^{2}_{0}(3 {x}^{2} + 4x + 3)dx$

$= \int \limits^{2}_{0}3 {x}^{2} \: dx + \int \limits^{2}_{0}4x \: dx +\int \limits^{2}_{0}3 \: dx$

$= 3\int \limits^{2}_{0}{x}^{2} \: dx +4 \int \limits^{2}_{0}x \: dx +3\int \limits^{2}_{0} \: dx$

$= 3 \bigg[ \frac{{x}^{3}}{3} \bigg ]^{2}_{0} +4 \bigg[ \frac{{x}^{2}}{2} \bigg ]^{2}_{0} +3 \bigg[ x \bigg ]^{2}_{0}$

$= 3 \bigg[ \frac{{2}^{3}}{3} - 0\bigg ]+4 \bigg[ \frac{{2}^{2}}{2} - 0\bigg ] +3 \bigg[ 2 - 0 \bigg ]$

$= 3 \times \frac{8}{3} +4 \times \frac{4}{2} +3 \times 2$

$= 8 +2 \times 4 +3 \times 2$

$= 8 +8 +6$

$= 22$