Basic properties of definite integrals (additivity and linearity)

Practice Questions

AP Calculus AB › Basic properties of definite integrals (additivity and linearity)

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

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

$\begin{align*}&\int_{-9}^{0}f(x)dx=62\&\int_{13}^{0}f(x)dx=-46\&\int_{18}^{13}f(x)dx=20\&\text{Use the above values to find }\int_{-9}^{18}f(x)dx\end{align*}$

$\begin{align*}&\int_{5}^{12}f(x)dx=99\&\int_{26}^{12}f(x)dx=-39\&\int_{0}^{26}f(x)dx=108\&\text{Calculate from the above values }\int_{5}^{0}f(x)dx\end{align*}$

Given that $\int_{5}^{1}(2u)dx = 8$ and $\int_{3}^{2}(-u)dx = 4$ , find the value of the following expression:

$\int_{1}^{3}(u)dx - \int_{5}^{4}(u)dx + \int_{2}^{4}(u)dx$

$\begin{align*}&\int_{0}^{13}f(x)dx=-60\&\int_{13}^{27}f(x)dx=-25\&\int_{45}^{34}f(x)dx=-22\&\int_{53}^{45}f(x)dx=16\&\int_{53}^{54}f(x)dx=-26\&\int_{0}^{54}f(x)dx=-86\&\text{Use the above values to find }\int_{27}^{34}f(x)dx\end{align*}$

$\begin{align*}&\int_{-5}^{8}f(x)dx=68\&\int_{10}^{8}f(x)dx=96\&\int_{10}^{22}f(x)dx=24\&\int_{-10}^{22}f(x)dx=-22\&\text{Calculate from the above values }\int_{-10}^{-5}f(x)dx\end{align*}$

$\begin{align*}&\int_{-4}^{6}f(x)dx=5\&\int_{12}^{6}f(x)dx=90\&\int_{15}^{12}f(x)dx=73\&\int_{19}^{15}f(x)dx=-70\&\int_{22}^{19}f(x)dx=97\&\int_{24}^{22}f(x)dx=36\&\text{Calculate from the above values }\int_{-4}^{24}f(x)dx\end{align*}$

$\begin{align*}&\int_{22}^{8}f(x)dx=-68\&\int_{22}^{28}f(x)dx=68\&\int_{28}^{29}f(x)dx=44\&\text{Calculate from the above values }\int_{8}^{29}f(x)dx\end{align*}$

$\begin{align*}&\int_{-3}^{9}f(x)dx=-67\&\int_{9}^{22}f(x)dx=74\&\int_{37}^{22}f(x)dx=-18\&\int_{39}^{37}f(x)dx=-67\&\int_{42}^{39}f(x)dx=68\&\int_{42}^{45}f(x)dx=86\&\text{Calculate from the above values }\int_{-3}^{45}f(x)dx\end{align*}$

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