Question

Find the particular antiderivative F(x) off(x) = 8x - 11 that satisfies F(1)= 12.

Answer 1

Step-by-step explanation

Given the function f(x)=8x-11, we are asked to find its anti-derivative F(x) that satisfies F(1)=12.

Therefore

`\begin{gathered} F(x)=\int f(x)dx=\int (8x-11)dx \\ =(8x^(1+1))/(1+1)-(11x^(0+1))/(0+1)+c \\ =(8x^2)/(2)-11x+c \\ =4x^2-11x+c \end{gathered}`

Next, we find the value of c

`\begin{gathered} at\text{ f(1)=12} \\ 4(1)^2-11(1)+c=12 \\ 4-11+c=12 \\ c=12+7 \\ c=19 \end{gathered}`

Therefore, we have;

Answer:

`F(x)=4x^2-11x+19`