Question Type 2: Integrating polynomials with boundary conditions to solve for C Exercises

Given $y' = 5x^2 + 3$ and $y(0)=1$, find $y(x)$.

Determine $y(x)$ if $y' = 9x^4 + 8x$ and $y(0)=7$.

If $y' = 5x^3 - 4x^2 + 7x - 2$ and $y(0)=5$, determine $y(x)$.

Given $y' = 3x^2 + 2x + 1$ with $y(2)=20$, find the function $y(x)$.

Determine $y(x)$ if $y' = 2x^3 + 5x^2 - x +4$ and $y(1)=3$.

Find the function $y(x)$ if $y' = -5x^3 + x - 1$ and $y(1)=-2$.

Given $y' = 8x^4 + 2x^3 + 11x + 3$ and the condition $y(1)=9$, find $y(x)$.

Find $y(x)$ given $y' = 7x^2 - 3x + 2$ and the condition $y(3)=50$.

If $y' = 4x^4 - x^3 + 6x$ and $y(-1)=0$, determine $y(x)$.

Find $y(x)$ if $y' = 6x^5 + x^2 - 3$ and $y(1)=10$.

If $y' = x^5 - 2x^3 + x$ and $y(2)=15$, determine $y(x)$.

If $y' = 2x^6 - x^4 + 4x^2 -2$ and $y(-2)=5$, determine $y(x)$.