Bài tập 11 trang 152 SGK Toán 12 NC
Bài tập 11 trang 152 SGK Toán 12 NC
Cho biết \(\int \limits_1^2 f\left( x \right)dx = - 4,\int\limits_1^5 {f(x)dx} = 6,\int\limits_1^5 {g(x)dx} = 8.\) Hãy tính
\(\begin{array}{l}
a)\int\limits_2^5 {f(x)dx} \\
b)\int\limits_1^2 {3f(x)dx} \\
c)\int\limits_1^5 {\left[ {f(x) - g(x)} \right]dx} \\
d)\int\limits_1^5 {\left[ {4f(x) - g(x)} \right]dx}
\end{array}\)
a)
\(\begin{array}{l}
\int\limits_2^5 {f(x)dx} = \int\limits_2^1 {f(x)dx} + \int\limits_1^5 {f(x)dx} \\
= - \int\limits_1^2 {f(x)dx} + \int\limits_1^5 {f(x)dx} \\
= 4 + 6 = 10
\end{array}\)
b)
\(\begin{array}{l}
\int\limits_1^2 {3f(x)dx} = 3\int\limits_1^2 {f(x)dx} \\
= 3.\left( { - 4} \right) = - 12
\end{array}\)
c)
\(\begin{array}{l}
\int\limits_1^5 {\left[ {f(x) - g(x)} \right]dx} \\
= \int\limits_1^5 {f(x)dx} - \int\limits_1^5 {g(x)dx} \\
= 6 - 8 = - 2
\end{array}\)
d)
\(\begin{array}{l}
\int\limits_1^5 {\left[ {4f(x) - g(x)} \right]dx} \\
= 4\int\limits_1^5 {f(x)dx} - \int\limits_1^5 {g(x)dx} \\
= 4.6 - 8 = 16
\end{array}\)
-- Mod Toán 12
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