What is the integral from 0 to 3 of ((30-y)-y^{1/3}) ?

The integral from 0 to 3 of ((30-y)-y^{1/3}) is 171/2-(9*3^{1/3})/4

Popular >

integral from 0 to 3 of ((30-y)-y^{1/3})

\int_{0}^{3} ((30 - y) - y^{\frac{1}{3}}) d y

\frac{171}{2} - \frac{9 \cdot 3 ^{\frac{1}{3}}}{4}

Decimal Notation

82.25493 \dots

Solution steps

\int_{0}^{3} 30 - y - y^{\frac{1}{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}^{3} 30 d y - \int_{0}^{3} y d y - \int_{0}^{3} y^{\frac{1}{3}} d y

\int_{0}^{3} 30 d y = 90

\int_{0}^{3} y d y = \frac{9}{2}

\int_{0}^{3} y^{\frac{1}{3}} d y = \frac{9 \cdot 3 ^{\frac{1}{3}}}{4}

= 90 - \frac{9}{2} - \frac{9 \cdot 3 ^{\frac{1}{3}}}{4}

Combine the fractions

90 - \frac{9}{2} : \frac{171}{2}

= \frac{171}{2} - \frac{9 \cdot 3 ^{\frac{1}{3}}}{4}

\frac{d}{d x} (sin (x) - e^{x})

y^{^{''}} + 2 y^{^{'}} + 2 y = sin (2 t), y (0) = 0, y^{^{'}} (0) = 0

\frac{d}{d r ( d )} ([\frac{12.61}{0.45} (84.4)] r (d) a d)

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

\int \frac{( tan ( x ) + sin ( x ) )}{sec ( x )} d x

What is the integral from 0 to 3 of ((30-y)-y^{1/3}) ?
The integral from 0 to 3 of ((30-y)-y^{1/3}) is 171/2-(9*3^{1/3})/4