### Calculus meets Functions

Package of problems

## Problem

Which of the integrals below can be evaluated if we know that

$\large{\int_0^3 f(x) \ dx = 7 \ \text{and} \ \int_0^3 g(x)\ dx =4\text{?}}$

$\int_0^3 (f(x)+2g(x))\ dx$

$\int_0^3 f(x)g(x)\ dx$

$\int_0^6 f(x) \ dx$

$\int_0^3 (g(x)+2) \ dx$

$\int_3^0 \!f(x) \ dx \, \times \int^3_0 \!g(x) \ dx$

$\int^3_{-3} g(x) \ dx$

$\int_{-3}^{3} f(x) \ dx$

$\int^2_{-1} f(x+1) \ dx$

Which of the integrals can be evaluated if we have the following extra information?

1. $f(x)$ is symmetric about $x=3$

2. $g(x)$ is an odd function

3. $f(x)$ is an even function