What is the integral from 0 to 2x of (2xy^3-x) ?

The integral from 0 to 2x of (2xy^3-x) is -2x^2+8x^5

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 0 to 2x of (2xy^3-x)

\int_{0}^{2 x} (2 x y^{3} - x) d y

- 2 x^{2} + 8 x^{5}

Solution steps

\int_{0}^{2 x} 2 x y^{3} - x d y

Apply the Sum Rule:

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

= - \int_{0}^{2 x} x d y + \int_{0}^{2 x} 2 x y^{3} d y

\int_{0}^{2 x} x d y = 2 x^{2}

\int_{0}^{2 x} 2 x y^{3} d y = 8 x^{5}

= - 2 x^{2} + 8 x^{5}

\int_{- 1}^{5} (4 x^{3} - 3 x^{2} + 1) d x

\int_{0}^{2} x e^{\frac{x ^{2}}{2}} d x

\int_{- 2}^{2} 10 4 - x^{2} d x

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

\int_{0}^{2} \frac{x ^{3}}{3} d x

What is the integral from 0 to 2x of (2xy^3-x) ?
The integral from 0 to 2x of (2xy^3-x) is -2x^2+8x^5