Step 1

Evaluate the integral:

\(\displaystyle{\int_{{-{7}}}^{{{6}}}}{e}^{{-{0.25}{x}}}{\left.{d}{x}\right.}=-{\frac{{{1}}}{{{0.25}}}}{{\left[{e}^{{-{0.25}{x}}}\right]}_{{-{7}}}^{{{6}}}}\)

\(\displaystyle=-{\frac{{{1}}}{{{0.25}}}}{\left[{e}^{{-{0.25}\times{6}}}-{e}^{{-{0.25}\times{\left(-{7}\right)}}}\right]}\)

\(\displaystyle={4}{\left({e}^{{{1.75}}}-{e}^{{-{1.5}}}\right)}\)

\(\displaystyle\approx{22.126}\)

Step 2

Thus, the integral equals 22.126.

Evaluate the integral:

\(\displaystyle{\int_{{-{7}}}^{{{6}}}}{e}^{{-{0.25}{x}}}{\left.{d}{x}\right.}=-{\frac{{{1}}}{{{0.25}}}}{{\left[{e}^{{-{0.25}{x}}}\right]}_{{-{7}}}^{{{6}}}}\)

\(\displaystyle=-{\frac{{{1}}}{{{0.25}}}}{\left[{e}^{{-{0.25}\times{6}}}-{e}^{{-{0.25}\times{\left(-{7}\right)}}}\right]}\)

\(\displaystyle={4}{\left({e}^{{{1.75}}}-{e}^{{-{1.5}}}\right)}\)

\(\displaystyle\approx{22.126}\)

Step 2

Thus, the integral equals 22.126.