Question

ASSIGNMENT

Evaluate -
$\sf \: \displaystyle\int_{ - 1}^{25}\sf {e}^{x - [x]}$
- Need help! ​

Answer 1

Answer:

26

Explanation:

$\int\limits^{25}_{-1} {e^{x-[x]}} \, dx$

simplify

$\int\limits^{25}_{-1} {e^{0} \, dx$

any variable to the power 0 is 1

$\int\limits^{25}_{-1} 1 \, dx$

integrating 1 gives x

$\left[ \:x \: \right]^{25}_{-1}$

apply limits

$25 - (-1)$

add terms

$26$

Answer 2

$\\ \rm\hookrightarrow \displaystyle\int\limits_{-1}^{25}e^{x-[x]}dx$

• [x] is x if x is a real number

$\\ \rm\hookrightarrow \displaystyle\int\limits_{-1}^{25}e^{x-x}dx$

$\\ \rm\hookrightarrow \displaystyle\int\limits_{-1}^{25}e^0dx$

• e⁰=1

$\\ \rm\hookrightarrow \displaystyle\int\limits_{-1}^{25}dx$

$\\ \rm\hookrightarrow \left[x\right]_{-1}^{25}$

$\\ \rm\hookrightarrow 25-(-1)$

$\\ \rm\hookrightarrow 25+1$

$\\ \rm\hookrightarrow 26$