Substitution

To substitute a number or new expression for a variable, enclose an expression in square brackets, enter an assignment for the variable in a subscript, and choose Evaluate.

$\blacktriangleright$ Evaluate

$\left[\vphantom{ x^{2}+2x-3}\right.$x2 + 2x - 3$\left.\vphantom{ x^{2}+2x-3}\right]_{{x=a}}^{}$ = a2 +2a - 3 6pt

$\left[\vphantom{ x^{2}+2x-3}\right.$x2 + 2x - 3$\left.\vphantom{ x^{2}+2x-3}\right]_{{x=5}}^{}$ = 32 6pt

$\left[\vphantom{ \frac{x^{2}-3x}{5}}\right.$${\frac{{x^{2}-3x}}{{5}}}$$\left.\vphantom{ \frac{x^{2}-3x}{5}}\right]_{{x=y-z}}^{}$ = ${\frac{{1}}{{5}}}$$\left(\vphantom{
y-z}\right.$y - z$\left.\vphantom{
y-z}\right)^{{2}}_{}$ - ${\frac{{3}}{{5}}}$y + ${\frac{{3}}{{5}}}$z

The expression in the subscript is an assignment for the variable on the left of the equals sign. Notice that, in particular, x = y + z, y = x - z and z = x - y are not equivalent assignments.

$\blacktriangleright$ Evaluate

$\left[\vphantom{ x+y}\right.$x + y$\left.\vphantom{ x+y}\right]_{{x=y+z}}^{}$ 6pt = 2y + z

$\left[\vphantom{ x+y}\right.$x + y$\left.\vphantom{ x+y}\right]_{{y=x-z}}^{}$ 6pt = 2x - z

$\left[\vphantom{ x+y}\right.$x + y$\left.\vphantom{ x+y}\right]_{{z=x-y}}^{}$ = x + y

To substitute two numbers or new expressions for a variable and find the difference, enclose an expression in square brackets

$\displaystyle \left[\vphantom{ x}\right.$x$\displaystyle \left.\vphantom{ x}\right]_{{x=a}}^{{x=b}}$

enter the numbers or new expressions in a subscript and superscript, and choose Evaluate.

$\blacktriangleright$ Evaluate

$\left[\vphantom{ x}\right.$x$\left.\vphantom{ x}\right]_{{x=a}}^{{x=b}}$ = b - a 4pt

$\left[\vphantom{ x^{2}+2x-3}\right.$x2 + 2x - 3$\left.\vphantom{ x^{2}+2x-3}\right]_{{x=a}}^{{x=b}}$ = b2 +2b - a2 -2a pt

$\left[\vphantom{ x^{2}+2x-3}\right.$x2 + 2x - 3$\left.\vphantom{ x^{2}+2x-3}\right]_{{x=3}}^{{x=5}}$ = 20

$\blacktriangleright$ Evaluate, Factor

$\left[\vphantom{ \frac{x^{2}-3x}{5}}\right.$${\frac{{x^{2}-3x}}{{5}}}$$\left.\vphantom{ \frac{x^{2}-3x}{5}}\right]_{{x=y-z}}^{{x=y+z}}$ = ${\frac{{1}}{{5}%
}}$$\left(\vphantom{ y+z}\right.$y + z$\left.\vphantom{ y+z}\right)^{{2}}_{}$ - ${\frac{{6}}{{5}}}$z - ${\frac{{1}}{{5}}}$$\left(\vphantom{
y-z}\right.$y - z$\left.\vphantom{
y-z}\right)^{{2}}_{}$ = ${\frac{{2}}{{5}}}$z$\left(\vphantom{ 2y-3}\right.$2y - 3$\left.\vphantom{ 2y-3}\right)$

From the expanding brackets panel, you can choose a nonprinting dashed vertical line for the left bracket; and a square bracket or vertical line for the right bracket. You can also enter from the keyboard a right vertical line only, with subscript, or with both subscript and superscript.

$\blacktriangleright$ Evaluate

$\left[\vphantom{ x^{2}-3}\right.$x2 - 3$\left.\vphantom{ x^{2}-3}\right]_{{x=a}}^{{x=b}}$ = b2 - a2 6pt

$\left.\vphantom{ x^{2}-3}\right.$x2 - 3$\left.\vphantom{ x^{2}-3}\right]_{{x=a}}^{{x=b}}$ = b2 - a2 6pt

$\left.\vphantom{ x^{2}-3}\right.$x2 - 3$\left.\vphantom{ x^{2}-3}\right\vert _{{x=a}}^{{x=b}}$ = b2 - a2 6pt

x + 3|x=y+z = y + z + 3 6pt

x + 3|x=y+zx=u-v = u - v - y - z



Subsections