given the following function: f(x)={( kx 0<X<10 k(20-x) 10<X<20 0 otherwise)┤ Find F(x) and its graph.

Since f(x) is a probability density function, then:
∫_(-∞)^∞〖f(x)dx=〗 1
∴1=∫_0^10〖kx dx〗+k∫_10^20〖(20-x)〗 dx
=k[1/2 x^2 ]_0^10+k[20x-1/2 x^2 ]_10^20
=50k+k[400-200-20+50]=100k→k=1/100
Thus:
f(x)={(  x/100               0<X<10 ((20-x))/100          10<X<20  0                      otherwise)┤
To evaluate the C.D.F:
If X<0 →  F(x)=0
If 0<X<10   ,then→  F(x)=∫_0^xt/100 dt=x^2/200
If 10<X<20   ,then→  F(x)=1/100 ∫_0^10〖tdt+1/100 ∫_10^x(20-t) 〗 dt
=1/100 [1/2 t^2 ]_0^10+1/100 [20t-1/2 t^2 ]_10^x
=1/100 [1/2  100]+1/100 [20x-1/2 x^2-200+50]
=1/2+1/100 [20x-1/2 x^2-150]
=x/5-x^2/200-1
Thus:
F(x)={(                0                        X<0                   x^2/200                         0<X<10x/5-x^2/100-1           10<X<20 1                      20<x)┤
Its graph is: