Terrie Lang

2021-12-28

Evaluate the definite integral.
${\int }_{2}^{3}{2}^{x}dx$

Stella Calderon

Step 1
To evaluate the given integral,
${\int }_{2}^{3}{2}^{x}dx$
Solution:
The given integral is, ${\int }_{2}^{3}{2}^{x}dx$
Solving integral we get,
${\int }_{2}^{3}{2}^{x}dx={\frac{{2}^{x}}{\mathrm{log}2}}_{2}^{3}$
$=\frac{{2}^{3}-{2}^{2}}{\mathrm{log}2}$
$=\frac{8-4}{\mathrm{log}2}$
Step 2
further solving we get,
${\int }_{2}^{3}{2}^{x}dx=4\mathrm{log}2$
Hence, the value of integral is $\frac{4}{\mathrm{log}2}$.

Kirsten Davis

Given:
${\int }_{2}^{3}{2}^{x}dx$
Integral of exponential function:
$\int {a}^{x}dx=\frac{{a}^{x}}{\mathrm{ln}\left(a\right)}$ at a=2:
$=\frac{{2}^{x}}{\mathrm{ln}\left(2\right)}$
$=\frac{{2}^{x}}{\mathrm{ln}\left(2\right)}+C$

Vasquez

${\int }_{2}^{3}{2}^{x}dx$
$\int {2}^{x}dx$
$\frac{{2}^{x}}{\mathrm{ln}\left(2\right)}$
Return the limits
$\frac{{2}^{x}}{\mathrm{ln}\left(2\right)}{|}_{2}^{3}$
Calculate the expression
$\frac{{2}^{3}}{\mathrm{ln}\left(2\right)}-\frac{{2}^{2}}{\mathrm{ln}\left(2\right)}$
Simplify
Solution
$\frac{4}{\mathrm{ln}\left(2\right)}$

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