[m]S= ∫_{1} ^{3}x^2dx=(\frac{x^3}{3})|_{1} ^{3}=\frac{3^3}{3}-\frac{1^3}{3}=\frac{27-1}{3}[/m]
б)
[m]S= ∫_{-\frac{π}{2}} ^{\frac{π}{2}}2cosx dx=2(sinx)|_{-\frac{π}{2}} ^{\frac{π}{2}}=2sin\frac{π}{2}-2sin(-\frac{π}{2})=2\cdot 1-2\cdot (-1)=4[/m]
в)
[m]S= ∫_{0} ^{2}(x^2-3x+4-(4-x))dx= ∫_{0} ^{2}(x^2-3x+4-4+x)dx=∫_{0} ^{2}(x^2-2x)dx=(\frac{x^3}{3}-x^2)∫_{0} ^{2}=...[/m]
г)
[m]S= ∫_{\frac{π}{4}} ^{\frac{π}{2}}(cosx-sinx) dx=(sinx-(-cosx))|_{\frac{π}{4}} ^{\frac{π}{2}}=...[/m]