What is the integral from 0 to 5/7 of 5x-7x^2 ?

The integral from 0 to 5/7 of 5x-7x^2 is 125/294

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integral from 0 to 5/7 of 5x-7x^2

\int_{0}^{\frac{5}{7}} 5 x - 7 x^{2} d x

\frac{125}{294}

Decimal Notation

0.42517 \dots

Solution steps

\int_{0}^{\frac{5}{7}} 5 x - 7 x^{2} 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}^{\frac{5}{7}} 5 x d x - \int_{0}^{\frac{5}{7}} 7 x^{2} d x

\int_{0}^{\frac{5}{7}} 5 x d x = \frac{125}{98}

\int_{0}^{\frac{5}{7}} 7 x^{2} d x = \frac{125}{147}

= \frac{125}{98} - \frac{125}{147}

Simplify

\frac{125}{98} - \frac{125}{147} : \frac{125}{294}

= \frac{125}{294}

x \to 0 + lim (x^{8 x})

\frac{3}{x - 4}

\frac{d}{d t} (9 t sin (π t))

\int x^{3} x^{2} - 3 d x

x \to \infty lim (8 x e^{\frac{1}{x}} - 8 x)

What is the integral from 0 to 5/7 of 5x-7x^2 ?
The integral from 0 to 5/7 of 5x-7x^2 is 125/294