Evaluating integrals Evaluate the following integral.

${\int}_{0}^{\mathrm{ln}2}{\int}_{{e}^{x}}^{2}dydx$

FobelloE
2021-10-13
Answered

Evaluating integrals Evaluate the following integral.

${\int}_{0}^{\mathrm{ln}2}{\int}_{{e}^{x}}^{2}dydx$

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SchulzD

Answered 2021-10-14
Author has **83** answers

Step 1

Concept:

The calculus helps in understanding the changes between values that are related by a function. It is used in different areas such as physics, biology and sociology and so on. The calculus is the language of engineers, scientists and economics.

Step 2

Given:

${\int}_{0}^{\mathrm{ln}2}{\int}_{{e}^{x}}^{2}dydx$

the objective is to integrate the given integral.

Step 3

${\int}_{0}^{\mathrm{ln}2}{\int}_{{e}^{x}}^{2}dydx$

On integrating

$\int}_{{e}^{x}}^{2}1dt=2-{e}^{x$

${\int}_{0}^{\mathrm{ln}2}{\int}_{{e}^{x}}^{2}1dydx={\int}_{0}^{\mathrm{ln}2}(2-{e}^{x})dx$

${\int}_{0}^{\mathrm{ln}2}(2-{e}^{x})dx=2\mathrm{ln}\left(2\right)-1$

${\int}_{0}^{\mathrm{ln}2}{\int}_{{e}^{x}}^{2}1dydx=2\mathrm{ln}\left(2\right)-1$

Concept:

The calculus helps in understanding the changes between values that are related by a function. It is used in different areas such as physics, biology and sociology and so on. The calculus is the language of engineers, scientists and economics.

Step 2

Given:

the objective is to integrate the given integral.

Step 3

On integrating

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