petrusrexcs

2021-12-31

Evaluate the definite integral.

${\int}_{2}^{7}{e}^{2-x}dx$

Juan Spiller

Beginner2022-01-01Added 38 answers

Step 1

The given integral is as follows.

${\int}_{2}^{7}{e}^{2-x}dx$

Let u=2-x. Then, du=-dx.

The Lower limit will be u=2-2=0 and the upper limit will be u=2-7=-5.

Step 2

Apply the substitutions and evaluate the integral as follows.

${\int}_{2}^{7}{e}^{2-x}dx={\int}_{0}^{-5}{e}^{u}(-du)$

$={\int}_{0}^{-5}-{e}^{u}du$

$=-{\left[{e}^{u}\right]}_{0}^{-5}$

$=-[{e}^{-5}-{e}^{0}]$

$=1-{e}^{-5}$

$=1-\frac{1}{{e}^{5}}$

Therefore, the value of the given integral is,

$1-\frac{1}{{e}^{5}}$

The given integral is as follows.

Let u=2-x. Then, du=-dx.

The Lower limit will be u=2-2=0 and the upper limit will be u=2-7=-5.

Step 2

Apply the substitutions and evaluate the integral as follows.

Therefore, the value of the given integral is,

yotaniwc

Beginner2022-01-02Added 34 answers

Evaluate the indefinite integral

Return the limits

Simplify

Answer:

Vasquez

Expert2022-01-07Added 669 answers

This is a tabular integral:

Let's calculate a definite integral:

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