What is the integral from x to 1 of 2(x+y) ?

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

Popular >

integral from x to 1 of 2(x+y)

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

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

Solution steps

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

Take the constant out:

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

= 2 \cdot \int_{x}^{1} x + y 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

= 2 (\int_{x}^{1} x d y + \int_{x}^{1} y d y)

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

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

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

Simplify

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

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

\frac{d ^{8}}{d x ^{8}} ((2 x + 5)^{7})

\frac{\partial}{\partial y} (2 x cos (y))

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

\int e^{x - 2 x} d x

x \to \infty lim ((x - 1) \cdot e^{\frac{1}{x - 1}})

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