find an antiderivative

Question

Find an antiderivative F(x)Fx with F′(x)=f(x)=8+15x2+21x6F'x=fx=8+15x2+21x6 and F(1)=0F1=0.

 

Remember to include a "+ C" if appropriate.

 

F(x)=Fx=

 

Answer 1

f(x) = 15x^2 +21x + 8

F(x) = 5x^3 +10.5x^2 + 8x + C

if F(1)=0

then 5+10.5+8+C =0

C= -23.5

and

F(x)= 5x^3 +10.5x^2 +8x -23.5