IB Mathematics Applications & Interpretation Question Type 1: Integrating a Polynomial Without Boundary Conditions Exercises

Evaluate the indefinite integral $\int (10x^2-5x+3)dx$.

Find $\int (x^3+2x^2+x+1)dx$.

If $\frac{dy}{dx}=2x^4-3x^2+1$ and $y(1)=3$, determine $y(x)$.

Find the particular solution of $\frac{dy}{dx}=8x^4+2x^3+11x+3$ given that $y(1)=9$.

Determine the function $y$ if $\frac{dy}{dx}=4x^3-x^2+6$ and $y(0)=5$.

Find the indefinite integral $\int (x^7-3x^5+2x^2)dx$.

Evaluate the indefinite integral of $3x^4-x^2+7$.

Compute $\int (6x^5-4x+2)dx$.

Given that $\frac{dy}{dx}=7x^3-2x+5$ and $y(2)=0$, find an expression for $y$ in terms of $x$.

Find the particular solution of $\frac{dy}{dx}=5x^5+4x^3-6x$ with the condition $y(0)=10$.

Find the particular solution of $\frac{dy}{dx}=3x^2+8$ satisfying the condition $y(1)=4$.

Find the indefinite integral of $5x^3+8x^2+9x+3$.