Evaluate the following integrals showing each step. displaymode int x e^x dx. displaymode int x sin 2x dx. displaymode int e^(-x) x^2 dx. displaymode int [ln x]/[x^2] dx. find the center of mass of the region bounded by y = sin x between x = 0 and x = pi above the x-axis. displaymode integral from 0^pi t sin 2t dt. displaymode integral from (0)^(pi^2n^2) sin root(x) dx. (first substitution, then by parts)

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

3

step-by-step explanation:

answer: 0

step-by-step explanation: the positive, like 5, + its opposite, like -5 would be 0

5+(-5)=0, or 5-5=0