What is the integral from 0 to 1 of 5/(1+p^2) ?

The integral from 0 to 1 of 5/(1+p^2) is (5pi)/4

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 0 to 1 of 5/(1+p^2)

\int_{0}^{1} \frac{5}{1 + p ^{2}} d p

\frac{5 π}{4}

Decimal

3.92699 \dots

Solution steps

\int_{0}^{1} \frac{5}{1 + p ^{2}} d p

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 5 \cdot \int_{0}^{1} \frac{1}{1 + p ^{2}} d p

Use the common integral:

\int \frac{1}{1 + p ^{2}} d p = arctan (p)

= 5 [arctan (p)]_{0}^{1}

Compute the boundaries:

\frac{π}{4}

= 5 \cdot \frac{π}{4}

Simplify

= \frac{5 π}{4}

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

\int_{0}^{1} 5 z^{4} d z

\int_{3}^{0} 15 w^{4} - 13 w^{2} + w d w

\int_{- 5}^{1} (- x^{2} - 3 x) d x

\int_{50}^{100} \frac{x}{20 + 3 x ^{2}} d x

What is the integral from 0 to 1 of 5/(1+p^2) ?
The integral from 0 to 1 of 5/(1+p^2) is (5pi)/4