What is the integral from pi/4 to pi/2 of csc(x) ?

The integral from pi/4 to pi/2 of csc(x) is -ln(sqrt(2)-1)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from pi/4 to pi/2 of csc(x)

\int_{\frac{π}{4}}^{\frac{π}{2}} csc (x) d x

- ln (2 - 1)

Decimal Notation

0.88137 \dots

Solution steps

\int_{\frac{π}{4}}^{\frac{π}{2}} csc (x) d x

Apply u-substitution

: \int_{2 - 1}^{1} \frac{1}{u} d u

= \int_{2 - 1}^{1} \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= [ln ∣ u ∣]_{2 - 1}^{1}

Compute the boundaries:

- ln (2 - 1)

= - ln (2 - 1)

\int_{0}^{4} \frac{x}{1 + x} d x

\int_{1}^{7} \frac{9}{1 + x ^{2}} d x

\int_{- 1}^{2} - \frac{4}{x ^{3}} d x

\int_{0}^{t} e^{4 t} d t

\int_{1}^{2} x^{2} - 5 x + 6 d x

What is the integral from pi/4 to pi/2 of csc(x) ?
The integral from pi/4 to pi/2 of csc(x) is -ln(sqrt(2)-1)