Question

Tolong bantuannya nomor 795

Answer 1

*)cari titik potong

-)x-2y = 0

-2y=-x

y=x/2

-)x²-2x+y=0

y=-x²+2x

-)y=y

x/2=-x²+2x

x=-2x²+4x

0=-2x²+3x

0=x(-2x+3)

maka:

x=0

dan

-2x+3=0

-2x=-3

x=3/2

y=x/2 = (3/2)/2 = 3/4

jadi titik potong = (3/2,3/4)

*)cari luas

Integral (-x²+2x)-(x/2) dx

= integral -x²+(3/2)x dx

=-x³/3 + (3/2)(1/2)x²

=-x³/3 + 3x²/4

=-(3/2)³/3 + 3(3/2)²/4

=-(27/8)/3 + 3(9/4)/4

=(-27/24) + (27/12)/4

=(-27/24) + (27/48)

=(-54/48) + (27/48)

=(-27/48)

=(-9/16)

jadi luasnya 9/16 (A)