Bài tập 46 trang 176 SGK Toán 12 NC
Bài tập 46 trang 176 SGK Toán 12 NC
Cho biết \(\int\limits_7^9 {f(x)dx} = - 1,\)
\(\int\limits_7^9 {f(x)dx} = 5,\int\limits_7^9 {g(x)dx} = 4.\)
Hãy tìm:
\(\begin{array}{l}
a)\int \limits_1^9 - 2f\left( x \right)dx\\
b)\int \limits_7^9 \left[ {f\left( x \right) + g\left( x \right)} \right]dx\\
c)\int\limits_7^9 {[2f(x) - 3g(x)]dx} \\
d)\int\limits_1^7 {f(x)dx}
\end{array}\)
a)
\(\begin{array}{l}
\int\limits_1^9 - 2f\left( x \right)dx = - 2\int\limits_1^9 f \left( x \right)dx\\
= - 2( - 1) = 2
\end{array}\)
b)
\(\begin{array}{l}
\int\limits_7^9 {\left[ {f\left( x \right) + g\left( x \right)} \right]} dx\\
= \int\limits_7^9 {f(x)dx} + \int\limits_7^9 {g(x)dx} \\
= 5 + 4 = 9
\end{array}\)
c)
\(\begin{array}{l}
\int\limits_7^9 {[2f(x) - 3g(x)]dx} \\
= 2\int\limits_7^9 {f(x)dx} - 3\int\limits_7^9 {g(x)dx} \\
= 2.5 - 3.4 = - 2
\end{array}\)
d)
\(\begin{array}{*{20}{l}}
{\int\limits_1^7 {f(x)dx} = \int\limits_1^9 {f(x)dx} + \int\limits_9^7 {f(x)dx} }\\
\begin{array}{l}
= \int\limits_1^9 {f(x)dx} - \int\limits_7^9 {f(x)dx} \\
= - 1 - 5 = - 6
\end{array}
\end{array}\)
-- Mod Toán 12
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