Property 21
\(\displaystyle\int\limits_a^b f(x)\cdot dx=S_1\)
\(-\displaystyle\int\limits_b^c f(x)\cdot dx=S_2\)
\(S_1=\displaystyle\int\limits_b^c f^{-1}(x)\cdot dx\)
\(S_2=-\displaystyle\int\limits_a^b f^{-1}(x)\cdot dx\)
1.
\(S_1=16\)
\(S_2=7\)
\(\Rightarrow\displaystyle\int\limits_{-3}^{5} f(x)\,dx=?\)
2.
\(S_1=4\)
\(S_2=10\)
\(\Rightarrow\displaystyle\int\limits_{-1}^{6} f(x)\,dx=?\)
3.
\(\displaystyle\int\limits_{-5}^{7} f(x)\,dx=10\)
\(S_1=2\)
\(S_2=4\)
\(S_4=3\)
\(\Rightarrow S_3=?\)