Answer
a. $1$
b. $-1$
c. $-\pi$
d. $\sqrt 2\pi$
e. $1-3\pi$
Work Step by Step
Given $\int_{0}^2f(x)dx=\pi$, $\int_{0}^27g(x)dx=7$, and $\int_{0}^1g(x)dx=2$, we have
a. $\int_{0}^2g(x)dx=7/7=1$
b. $\int_{1}^2g(x)dx=$\int_{0}^2g(x)dx+$\int_{0}^1g(x)dx=1-2=-1$
c. $\int_{2}^0f(x)dx=-\int_{0}^2f(x)dx=-\pi$
d. $\int_{0}^2\sqrt 2f(x)dx=\sqrt 2\int_{0}^2f(x)dx=\sqrt 2\pi$
e. $\int_{0}^2(g(x)-3f(x))dx=\int_{0}^2g(x)dx-3\int_{0}^2f(x)dx=1-3\pi$
