Question

ajutati ma va rog!!!

Answer 1

$\int_{ - 1}^{1}( {x}^{4} + 3 {x}^{2} + 5) \: dx$

$\int( {x}^{4} + 3 {x}^{2} + 5) \: dx$

$= \int {x}^{4} \: dx + \int3 {x}^{2} \: dx + \int5 \: dx$

$= \int {x}^{4} \: dx + 3 \int {x}^{2} \: dx + 5 \int1 \: dx$

$= \frac{ {x}^{4 + 1} }{4 + 1} + 3 \times \frac{ {x}^{2 + 1} }{2 + 1} + 5x$

$= \frac{ {x}^{5} }{5} + \frac{3 {x}^{3} }{3} + 5x$

$= \frac{ {x}^{5} }{5} + {x}^{3} + 5x + C$

$\int_{ - 1}^{1}( {x}^{4} + 3 {x}^{2} + 5) \: dx$

$= \frac{ {x}^{5} }{5} | _{ - 1}^{1} + {x}^{3} \ |_{ - 1}^{1} + 5x\ |_{ - 1}^{1}$

$= \frac{ {1}^{5} }{5} - \frac{ {( - 1)}^{5} }{5} + {1}^{3} - {( - 1)}^{3} + 5 \times 1 - 5 \times ( - 1)$

$= \frac{1}{5} - \frac{ - 1}{5} + 1 - ( - 1) + 5 + 5$

$= \frac{1}{5} + \frac{1}{5} + 1 + 1 + 5 + 5$

$= \frac{2}{5} + 2 + 10$

$= \frac{2 + 10 + 50}{5}$

$= \frac{62}{5}$