What is the integral from-1 to 0 of e^xcos(e^x) ?

The integral from-1 to 0 of e^xcos(e^x) is sin(1)-sin(1/e)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from-1 to 0 of e^xcos(e^x)

\int_{- 1}^{0} e^{x} cos (e^{x}) d x

sin (1) - sin (\frac{1}{e})

Decimal Notation

0.48183 \dots

Solution steps

\int_{- 1}^{0} e^{x} cos (e^{x}) d x

Apply u-substitution

: \int_{\frac{1}{e}}^{1} cos (u) d u

= \int_{\frac{1}{e}}^{1} cos (u) d u

Use the common integral:

\int cos (u) d u = sin (u)

= [sin (u)]_{\frac{1}{e}}^{1}

Compute the boundaries:

sin (1) - sin (\frac{1}{e})

= sin (1) - sin (\frac{1}{e})

\int_{- 1}^{2} 2 x + 3 d x

\int_{0}^{\frac{π}{2}} ∣ 6 sin (x) - 6 cos (2 x) ∣ d x

\int_{0}^{6} 6 x d x

\int_{0}^{x} 9 t e^{3 t} d t

\int_{0}^{0.64} ln (1 + x) d x

What is the integral from-1 to 0 of e^xcos(e^x) ?
The integral from-1 to 0 of e^xcos(e^x) is sin(1)-sin(1/e)