Problems
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- Determine an antiderivative of $f(x)=125x^{24}+32x^2-16x+2$.
- Determine an antiderivative of $f(x)=16x^3+6x^2+2x+7$.
- Determine an antiderivative of $f(x)=x^3+3x^2-8x-2$.
- Determine an antiderivative of $f(x)=4x+4$.
- Determine an antiderivative of $f(x)=x^{16}+3x^5+101$.
- Determine an antiderivative of $f(x)=2x^2-7x+11$.
- Prove that an antiderivative of a polynomial $f(x)=a_nx^n+a_{n-1}x^{n-1}+\cdots +a_0$ is \begin{eqnarray} F(x)&=&\frac{a_n}{n+1}x^{n+1}+\frac{a_{n-1}}{n}x^n\\ &+&\cdots +a_0x+C. \end{eqnarray}
- Determine an antiderivative of $f(x)=5x^2+3x-10$.
- Prove that if $F(x)$ and $G(x)$ are antiderivatives of $f(x)$, then there exists a constant such that $F(x)-G(x)=C$.
- Prove that if $F(x)$ is an antiderivative of $f(x)$ and $C$ is a constant, then $G(X)=F(x)+C$ is also an antiderivative of $f(x)$.
