Question

for a particular function, dy/dx=8x-5. if it is known that when x= 2,y= 8,find y in terms of x

Answer 1

$$\dfrac{dy}{dx}=8x-5$$

$$y=\int(8x-5)dx=4x^2-5x+C$$

Given $y(2)=8$

$$8=4(2)^2-5(2)+C$$

$$C=2$$

$$y(x)=4x^2-5x+2$$