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Popular >

integral of 2(y-1)

Solution

\int 2 (y - 1) d y

Solution

y^{2} - 2 y + C

Solution steps

\int 2 (y - 1) d y

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 2 \cdot \int y - 1 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

= 2 (\int y d y - \int 1 d y)

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

\int 1 d y = y

= 2 (\frac{y ^{2}}{2} - y)

Simplify

2 (\frac{y ^{2}}{2} - y) : y^{2} - 2 y

= y^{2} - 2 y

Add a constant to the solution

= y^{2} - 2 y + C

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\int x^{2} cos (n x) d x

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\int csc^{4} (2 x) d x

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\int \frac{9 + 5 x}{1 + x ^{2}} d x

Frequently Asked Questions (FAQ)

What is the integral of 2(y-1) ?
The integral of 2(y-1) is y^2-2y+C