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Popular >

integral from 0 to y-z of 2x-y

Solution

\int_{0}^{y - z} 2 x - y d x

Solution

- zy + z^{2}

Solution steps

\int_{0}^{y - z} 2 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_{0}^{- z + y} y d x + \int_{0}^{- z + y} 2 x d x

\int_{0}^{- z + y} y d x = y (y - z)

\int_{0}^{- z + y} 2 x d x = (y - z)^{2}

= - y (y - z) + (y - z)^{2}

Simplify

- y (y - z) + (y - z)^{2} : - zy + z^{2}

= - zy + z^{2}

Popular Examples

integral from-4 to 4 of (4+sqrt(16-x^2))

\int_{- 4}^{4} (4 + 16 - x^{2}) d x

integral from 1 to x^2 of e^{t^2}

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

integral from 2 to 5 of e^x

\int_{2}^{5} e^{x} d x

integral from 0 to 4 of (3x^2-2x+1)

\int_{0}^{4} (3 x^{2} - 2 x + 1) d x

integral from sqrt(8) to 4sqrt(8 of) 1/x

\int_{8}^{48} \frac{1}{x} d x

Frequently Asked Questions (FAQ)

What is the integral from 0 to y-z of 2x-y ?
The integral from 0 to y-z of 2x-y is -zy+z^2