What is the integral from x^2 to x of (1+2y) ?

The integral from x^2 to x of (1+2y) is x-x^4

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integral from x^2 to x of (1+2y)

\int_{x^{2}}^{x} (1 + 2 y) d y

x - x^{4}

Solution steps

\int_{x^{2}}^{x} 1 + 2 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_{x^{2}}^{x} 1 d y + \int_{x^{2}}^{x} 2 y d y

\int_{x^{2}}^{x} 1 d y = x - x^{2}

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

= x - x^{2} + x^{2} - x^{4}

Simplify

= x - x^{4}

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What is the integral from x^2 to x of (1+2y) ?
The integral from x^2 to x of (1+2y) is x-x^4