What is the integral from-1 to 1 of x+3sqrt(1-x^2) ?

The integral from-1 to 1 of x+3sqrt(1-x^2) is (3pi)/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from-1 to 1 of x+3sqrt(1-x^2)

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

\frac{3 π}{2}

Decimal

4.71238 \dots

Solution steps

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

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

\int_{- 1}^{1} x d x = 0

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

= 0 + \frac{3 π}{2}

Simplify

= \frac{3 π}{2}

\int_{4}^{x} \frac{1}{1 + x ^{3}} d x

\int_{0}^{\infty} e^{c t} d t

\int_{0}^{5} (\frac{x ^{2}}{3} + 1) d x

\int_{- 1}^{1} \frac{x + 2}{56} d x

\int_{1}^{\infty} c e^{- x} d x

What is the integral from-1 to 1 of x+3sqrt(1-x^2) ?
The integral from-1 to 1 of x+3sqrt(1-x^2) is (3pi)/2