Question

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

Answer 1

Explanation

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

Therefore

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

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:

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