What is the integral from 0 to pi/4 of sec^2(x)e^{tan(x)} ?

The integral from 0 to pi/4 of sec^2(x)e^{tan(x)} is e-1

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 0 to pi/4 of sec^2(x)e^{tan(x)}

\int_{0}^{\frac{π}{4}} sec^{2} (x) e^{t a n (x)} d x

e - 1

Decimal

1.71828 \dots

Solution steps

\int_{0}^{\frac{π}{4}} sec^{2} (x) e^{t a n (x)} d x

Apply u-substitution

: \int_{0}^{1} e^{u} d u

= \int_{0}^{1} e^{u} d u

Use the common integral:

\int e^{u} d u = e^{u}

= [e^{u}]_{0}^{1}

Compute the boundaries:

e - 1

= e - 1

\int_{2}^{x} t^{4} d t

\int_{3}^{8} 1 d x

\int_{0}^{1} (7 x^{2} - 4 x + 6) d x

\int_{- 7}^{1} x 2 - x d x

\int_{- 1}^{2} [(x^{2}) - (x + 2)] d x

What is the integral from 0 to pi/4 of sec^2(x)e^{tan(x)} ?
The integral from 0 to pi/4 of sec^2(x)e^{tan(x)} is e-1