What is the integral from x to 2-x of 6x^2y ?

The integral from x to 2-x of 6x^2y is 12x^2(-x+1)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from x to 2-x of 6x^2y

\int_{x}^{2 - x} 6 x^{2} y d y

12 x^{2} (- x + 1)

Solution steps

\int_{x}^{2 - x} 6 x^{2} y d y

Take the constant out:

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

= 6 x^{2} \cdot \int_{x}^{2 - x} y d y

Apply the Power Rule

: [\frac{y ^{2}}{2}]_{x}^{2 - x}

= 6 x^{2} [\frac{y ^{2}}{2}]_{x}^{2 - x}

Compute the boundaries:

\frac{( 2 - x ) ^{2}}{2} - \frac{x ^{2}}{2}

= 6 x^{2} (\frac{( 2 - x ) ^{2}}{2} - \frac{x ^{2}}{2})

Simplify

= 12 x^{2} (- x + 1)

\int_{6}^{11} (4 - 10 e^{- 0.2 x}) d x

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

\int_{0}^{1} (- x + 1) d x

\int_{0}^{5} t^{2} - t d t

What is the integral from x to 2-x of 6x^2y ?
The integral from x to 2-x of 6x^2y is 12x^2(-x+1)