What is the integral from x to 1 of y^2-2y+1 ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from x to 1 of y^2-2y+1

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

x^{2} - x + \frac{- x ^{3} + 1}{3}

Solution steps

\int_{x}^{1} y^{2} - 2 y + 1 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_{x}^{1} y^{2} d y - \int_{x}^{1} 2 y d y + \int_{x}^{1} 1 d y

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

\int_{x}^{1} 2 y d y = 1 - x^{2}

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

= \frac{1 - x ^{3}}{3} - (1 - x^{2}) + 1 - x

Simplify

= x^{2} - x + \frac{- x ^{3} + 1}{3}

\int_{0}^{1} \frac{1}{9 + 16 r ^{2}} d r

\int_{- H}^{H} cos (\frac{y π}{2 H}) d y

\int_{- 2}^{2} (4 - t^{2}) d t

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

\int_{0}^{12} x (0.1 e^{- 0.1 x}) d x

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