Question

Cho $\int_0^3 f(x) d x=5$ và $\int_0^3 g(x) d x=2$. Tính:
a) $\int_0^3[f(x)+g(x)] d x$;
b) $\int_0^3[f(x)-g(x)] d x$;
c) $\int_0^3 3 f(x) d x$
d) $\int_0^3[2 f(x)-3 g(x)] d x$.

Answer 1

a) \(\int\limits_0^3 {\left[ {f\left( x \right) + g\left( x \right)} \right]dx}  = \int\limits_0^3 {f\left( x \right)dx}  + \int\limits_0^3 {g\left( x \right)dx}  = 5 + 2 = 7\)

b) \(\int\limits_0^3 {\left[ {f\left( x \right) - g\left( x \right)} \right]dx}  = \int\limits_0^3 {f\left( x \right)dx}  - \int\limits_0^3 {g\left( x \right)dx}  = 5 - 2 = 3\)

c) \(\int\limits_0^3 {3f\left( x \right)dx}  = 3\int\limits_0^3 {f\left( x \right)dx}  = 3.5 = 15\)

d) \(\int\limits_0^3 {\left[ {2f\left( x \right) - 3g\left( x \right)} \right]dx}  = 2\int\limits_0^3 {f\left( x \right)dx}  - 3\int\limits_0^3 {g\left( x \right)dx}  = 2.5 - 3.2 = 4\)