Integration & Antiderivatives (College Board AP® Calculus AB): Exam Questions

$\int \frac{6x^2-5}{2x}dx=$

$\int \left(3x^2+1\right)\left(2x-1\right)dx=$

$\int \frac{1}{\sqrt{x}}\left(\frac{x+1}{x}\right)dx=$

The curve with equation $y=f\left(x\right)$ goes through the point $\left(3,5\right)$. Given that $\frac{dy}{dx}=2x^2-1$, what is $f\left(x\right)$?

The derivative of a function $f$ is $f^{\text{'}}\left(x\right)=\frac{3}{2\sqrt{x}}-2x$.

Given that $f\left(4\right)=-8$, what is $f\left(x\right)$?

A curve has slope $4x-5$ at each point $\left(x,y\right)$ on the curve. Given that this curve passes through the point $\left(1,3\right)$, which of the following is an equation for the curve.

If $f$ is a linear function, then $\int f^{\text{'}\text{'}}\left(x\right)dx=$

$\int \frac{x^2}{x^2+1}dx=$

A function $f$ has its derivative given by $f^{\text{'}}\left(x\right)=\frac{3-x}{x^2}$. Given that $f\left(1\right)=2$, what is $f\left(x\right)$?

A function $f$ satisfies $f\left(x\right)=\int \frac{2+5\sqrt{1-x^2}}{\sqrt{1-x^2}}dx$. Given that $f\left(1\right)=5$, what is the value of $f\left(0\right)$?

The curve with equation $y=f\left(x\right)$ goes through the point $\left(0,-\frac{45}{32\ln 2}\right)$. Given that $\frac{dy}{dx}=3·2^{4x-3}$, what is the value of $f\left(1\right)$?