What is the integral from 0 to 1 of 4-y-2sqrt(y)-1 ?

The integral from 0 to 1 of 4-y-2sqrt(y)-1 is 7/6

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integral from 0 to 1 of 4-y-2sqrt(y)-1

\int_{0}^{1} 4 - y - 2 y - 1 d y

\frac{7}{6}

Decimal

1.16666 \dots

Solution steps

\int_{0}^{1} 4 - y - 2 y - 1 d y

Simplify

= \int_{0}^{1} - y - 2 y + 3 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_{0}^{1} y d y - \int_{0}^{1} 2 y d y + \int_{0}^{1} 3 d y

\int_{0}^{1} y d y = \frac{1}{2}

\int_{0}^{1} 2 y d y = \frac{4}{3}

\int_{0}^{1} 3 d y = 3

= - \frac{1}{2} - \frac{4}{3} + 3

Simplify

- \frac{1}{2} - \frac{4}{3} + 3 : \frac{7}{6}

= \frac{7}{6}

\int (3 x^{2} + 2) (2 x^{3} + 4 x + 1)^{\frac{1}{2}} d x

x^{2} (\frac{d y}{d x}) - 2 x y = 3 y^{4}

\frac{d}{d x} (3 + x)

\frac{d y}{d x} = 0.6 y

\int e^{x^{3}} \cdot x^{2} d x

What is the integral from 0 to 1 of 4-y-2sqrt(y)-1 ?
The integral from 0 to 1 of 4-y-2sqrt(y)-1 is 7/6