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Popular >

integral from y to 3y of (x+y)

Solution

\int_{y}^{3 y} (x + y) d x

Solution

6 y^{2}

Solution steps

\int_{y}^{3 y} x + 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}^{3 y} y d x + \int_{y}^{3 y} x d x

\int_{y}^{3 y} y d x = 2 y^{2}

\int_{y}^{3 y} x d x = 4 y^{2}

= 2 y^{2} + 4 y^{2}

Simplify

= 6 y^{2}

Popular Examples

integral from 0 to 4 of t

\int_{0}^{4} t d t

integral from-1 to 5 of (2x-5)

\int_{- 1}^{5} (2 x - 5) d x

integral from 1 to 4 of 3/(1-2x)

\int_{1}^{4} \frac{3}{1 - 2 x} d x

integral from a to b of 2

\int_{a}^{b} 2 d x

integral from 1 to 2 of (3x-5)^2

\int_{1}^{2} (3 x - 5)^{2} d x

Frequently Asked Questions (FAQ)

What is the integral from y to 3y of (x+y) ?
The integral from y to 3y of (x+y) is 6y^2