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Popular >

integral from 2x to 2 of (x-y)

Solution

\int_{2 x}^{2} (x - y) d y

Solution

2 x - 2

Solution steps

\int_{2 x}^{2} 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

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

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

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

= x \cdot 2 - 2 x^{2} - (2 - 2 x^{2})

Simplify

x \cdot 2 - 2 x^{2} - (2 - 2 x^{2}) : 2 x - 2

= 2 x - 2

Popular Examples

integral from 0 to 3 of x^2-x-3

\int_{0}^{3} x^{2} - x - 3 d x

integral from x to 1 of 1/x

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

integral from 0 to 2 of 8*2^{-x}-2

\int_{0}^{2} 8 \cdot 2^{- x} - 2 d x

integral from-1 to 1 of (|x|-1/2)^2

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

integral from 1 to 6 of (-x^2+7x-6)

\int_{1}^{6} (- x^{2} + 7 x - 6) d x

Frequently Asked Questions (FAQ)

What is the integral from 2x to 2 of (x-y) ?
The integral from 2x to 2 of (x-y) is 2x-2