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Popular >

integral from 0 to 1 of x(x+y)

Solution

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

Solution

\frac{y}{2} + \frac{1}{3}

Solution steps

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

Expand

(y + x) x : y x + x^{2}

= \int_{0}^{1} y x + x^{2} 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_{0}^{1} y x d x + \int_{0}^{1} x^{2} d x

\int_{0}^{1} y x d x = \frac{y}{2}

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

= \frac{y}{2} + \frac{1}{3}

Popular Examples

integral from 1 to 4 of (1-x^2)

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

integral from 0 to 6 of 5

\int_{0}^{6} 5 d x

integral from 0 to 1 of x-1/2

\int_{0}^{1} x - \frac{1}{2} d x

integral from-1 to 1 of (2x^4sin(x))

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

integral from 1 to 3 of 6-2x

\int_{1}^{3} 6 - 2 x d x

Frequently Asked Questions (FAQ)

What is the integral from 0 to 1 of x(x+y) ?
The integral from 0 to 1 of x(x+y) is y/2+1/3