IB Mathematics Applications & Interpretation Question Type 2: Integrating Polynomials with Boundary Conditions to Solve for C Exercises

Find the function $y(x)$ if $y^{\prime }=-5x^3+x-1$ and $y(1)=-2$.

If $y^{\prime }=4x^4-x^3+6x$ and $y(-1)=0$, determine an expression for $y(x)$.

Given $y^{\prime }=8x^4+2x^3+11x+3$ and the initial condition $y(1)=9$, find $y(x)$.

Find $y(x)$ given $y^{\prime }=7x^2-3x+2$ and the condition $y(3)=50$.

Determine $y(x)$ if $y^{\prime }=2x^3+5x^2-x+4$ and $y(1)=3$.

Given that $y^{\prime }=2x^6-x^4+4x^2-2$ and $y(-2)=5$, find an expression for $y$ in terms of $x$.

Given $y^{\prime }=5x^2+3$ and $y(0)=1$, find $y(x)$.

Find $y(x)$ if $y^{\prime }=6x^5+x^2-3$ and $y(1)=10$.

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

Given $y^{\prime }=3x^2+2x+1$ with $y(2)=20$, find the function $y(x)$.

Given that $y^{\prime }=x^5-2x^3+x$ and $y(2)=15$, determine an expression for $y$ in terms of $x$.

Determine $y(x)$ if $y^{\prime }=9x^4+8x$ and $y(0)=7$.