Question

помогите с 16 17 18​

Answer 1

$16)\; \; \int\limits^{\frac{1}{2}}_{\frac{1}{2}}\, 3(x^2+1)\, dx=0\; \; ,\; \; t.k.\; \; a=b=\frac{1}{2}\\\\\\17)\; \; \int\limits^2_1\, 2\pi (1+x^2)\, dx=2\pi (x+\frac{x^3}{3})\Big |_1^2=2\pi \cdot (2+\frac{8}{3}-1-\frac{1}{3})=2\pi \cdot \frac{10}{3}=\frac{20\pi }{3}\\\\\\18)\; \; \int\limits^{a}_0\, (x^2-ax)\, dx=(\frac{x^3}{3}-a\cdot \frac{x^2}{2})\Big |^{a}_0=\frac{a^3}{3}-\frac{a^3}{2}=-\frac{a^3}{6}$