### Home > CALC > Chapter 4 > Lesson 4.1.1 > Problem4-7

4-7.

Examine $f(x)$ graphed at right.

1. Is $f(x)$ even, odd, or neither?

Even functions have reflective symmetry across the $y$-axis. Odd functions have rotational symmetry about the origin.

2. If $\int _ { 0 } ^ { 2 } f ( x ) d x = 10$, what is $\int _ { - 2 } ^ { 2 } f ( x ) d x$? Explain.

$\int_{0}^{2}f(x)dx = 10$ means the exact area under $f(x)$ between $x=-2$ and $x=2$ is $10$.

3. If $\int _ { 0 } ^ { 3 } f ( x ) d x = - 2$ and $\int _ { 0 } ^ { 2 } f ( x ) d x = 10$ find $\int _ { 2 } ^ { 3 } f ( x ) d x$. Explain.

$\int_{2}^{3}f(x)dx=\int_{0}^{3}f(x)dx-\int_{0}^{2}f(x)dx=$

4. If you know that $\int _ { 0 } ^ { 3 } f ( x ) d x$ and $\int _ { - 2 } ^ { 2 } f ( x ) d x$, how can you find $\int _ { 2 } ^ { 3 } f ( x ) d x$? Justify your process with a diagram, if necessary.

Refer to the steps in part (c) for more guidance.