given the following function: f(x)={( kx 0<X<10 k(20-x) 10<X<20 0 otherwise)┤ Calculate P(X>10) ,P(5≤X≤15)

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)┤
    P(X>10)
=1-P(X<10)
=1-F(10)=1-1/2=1/3
P(5<X<15)
=F(15)-F(5)=15/5-225/200-1-25/200
=3-1-250/200=2-5/4=3/4