What is the integral from x to 1 of 10xy^2 ?

The integral from x to 1 of 10xy^2 is (10x(1-x^3))/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 10xy^2

\int_{x}^{1} 10 x y^{2} d y

\frac{10 x ( 1 - x ^{3} )}{3}

Solution steps

\int_{x}^{1} 10 x y^{2} d y

Take the constant out:

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

= 10 x \cdot \int_{x}^{1} y^{2} d y

Apply the Power Rule

: [\frac{y ^{3}}{3}]_{x}^{1}

= 10 x [\frac{y ^{3}}{3}]_{x}^{1}

Compute the boundaries:

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

= 10 x (\frac{1}{3} - \frac{x ^{3}}{3})

Simplify

= \frac{10 x ( 1 - x ^{3} )}{3}

\int_{- 1}^{x} e^{t^{2}} d t

\int_{1}^{4} 4 d x

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

\int_{0}^{1} (7 x - 7^{x}) d x

\int_{- 5}^{7} ∣ x ∣ d x

What is the integral from x to 1 of 10xy^2 ?
The integral from x to 1 of 10xy^2 is (10x(1-x^3))/3