Use integration by parts to find the integrals in exercise.
∫xex dx.

Step-by-step explanation:

using the formular for integration by parts;

∫udv = uv -∫vdu   ..............equ 1

in the equation below;

∫

u=x , dv =

du= 1  v=

Substitute into equ 1

∫udv = - ∫

∫udv = -

50-38=12

step-by-step explanation:

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is