Integrals

Practice Questions

AP Calculus AB › Integrals

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$\begin{align*}&\text{The function }f(x)\text{ has the following values on the interval }x=[1,11]:\&f(1)=10\&f(3)=3\&f(5)=-13\&f(7)=4\&f(9)=-8\&f(11)=-15\&\text{Approximate the integral of }f(x)\text{ on this interval using right Riemann sums.}\end{align*}$

A particle at the origin has an initial velocity of . If its acceleration is given by , find the position of the particle after 1 second.

$\begin{align*}&\text{Approximate }\int_{5}^{13}f(x)\&\text{Using a left Riemann sum, if }f(x)\text{ has the values:}\&f(5)=-7\&f(7)=-8\&f(9)=-18\&f(11)=-8\&f(13)=-19\end{align*}$

Find the equation of the tangent line at when

$y=\frac{x^{3}-2x(x^{1/2})}{x}$

$\begin{align*}&\int_{10}^{19}f(x)dx=-40\&\int_{19}^{30}f(x)dx=1\&\int_{42}^{30}f(x)dx=-12\&\int_{4}^{42}f(x)dx=-19\&\text{Use the above values to find }\int_{10}^{4}f(x)dx\end{align*}$

$\begin{align*}&f(-10)=-19\&f(-3)=7\&f(4)=4\&f(11)=1\&\text{Approximate, using a left Riemann sum, }\int_{-10}^{11}f(x)\end{align*}$

$\begin{align*}&\text{The function }f(x)\text{ has the following values on the interval }x=[-8,2]:\&f(-8)=2\&f(-6)=-1\&f(-4)=16\&f(-2)=12\&f(0)=10\&f(2)=-18\&\text{Approximate the integral of }f(x)\text{ on this interval using left Riemann sums.}\end{align*}$

$\begin{align*}&\int_{13}^{4}f(x)dx=42\&\int_{17}^{13}f(x)dx=-56\&\int_{17}^{28}f(x)dx=35\&\int_{28}^{33}f(x)dx=-99\&\int_{4}^{48}f(x)dx=-10\&\text{Determine }\int_{48}^{33}f(x)dx\end{align*}$

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