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Popular >

integral of (y-x)

Solution

\int (y - x) d x

Solution

y x - \frac{x ^{2}}{2} + C

Solution steps

\int y - x 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 d x - \int x d x

\int y d x = y x

\int x d x = \frac{x ^{2}}{2}

= y x - \frac{x ^{2}}{2}

Add a constant to the solution

= y x - \frac{x ^{2}}{2} + C

Popular Examples

limit as x approaches-1 of (x^2-1)/(x-1)

x \to - 1 lim (\frac{x ^{2} - 1}{x - 1})

integral of (2v^3-v)/(v^4-v^2)

\int \frac{2 v ^{3} - v}{v ^{4} - v ^{2}} d v

xy^2(dy)/(dx)=y^3-x^2

x y^{2} \frac{d y}{d x} = y^{3} - x^{2}

integral of ((e^{2x}))/(49+e^{4x)}

\int \frac{( e ^{2 x} )}{49 + e ^{4 x}} d x

(d^2)/(dx^2)(x^{6/7}+5x)

\frac{d ^{2}}{d x ^{2}} (x^{\frac{6}{7}} + 5 x)

Frequently Asked Questions (FAQ)

What is the integral of (y-x) ?
The integral of (y-x) is yx-(x^2)/2+C