What is the integral from y to 2y of (8x+e^y) ?

The integral from y to 2y of (8x+e^y) is ye^y+12y^2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from y to 2y of (8x+e^y)

\int_{y}^{2 y} (8 x + e^{y}) d x

y e^{y} + 12 y^{2}

Solution steps

\int_{y}^{2 y} 8 x + e^{y} 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_{y}^{2 y} e^{y} d x + \int_{y}^{2 y} 8 x d x

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

\int_{y}^{2 y} 8 x d x = 12 y^{2}

= y e^{y} + 12 y^{2}

\int_{50}^{100} \frac{x}{16 + 5 x ^{2}} d x

\int_{0}^{4} (4 x - 1)^{2} d x

\int_{0}^{8} \frac{1}{2 x ^{\frac{1}{3}}} d x

\int_{0}^{2} (- x^{4} + 2 x^{2} + 8) d x

\int_{0}^{5} 3 x - 8 d x

What is the integral from y to 2y of (8x+e^y) ?
The integral from y to 2y of (8x+e^y) is ye^y+12y^2