What is the integral from-3 to 5 of [2y-(y^2-15)] ?

The integral from-3 to 5 of [2y-(y^2-15)] is 256/3

Popular >

integral from-3 to 5 of [2y-(y^2-15)]

\int_{- 3}^{5} [2 y - (y^{2} - 15)] d y

\frac{256}{3}

Decimal Notation

85.33333 \dots

Solution steps

\int_{- 3}^{5} 2 y - (y^{2} - 15) d y

Simplify

= \int_{- 3}^{5} 2 y - y^{2} + 15 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_{- 3}^{5} 2 y d y - \int_{- 3}^{5} y^{2} d y + \int_{- 3}^{5} 15 d y

\int_{- 3}^{5} 2 y d y = 16

\int_{- 3}^{5} y^{2} d y = \frac{152}{3}

\int_{- 3}^{5} 15 d y = 120

= 16 - \frac{152}{3} + 120

Simplify

16 - \frac{152}{3} + 120 : \frac{256}{3}

= \frac{256}{3}

\int_{0}^{1} (x^{2} + 1)^{5} x^{3} d x

\int_{- 1}^{0} (8 x - e^{x}) d x

\int_{0}^{1} \frac{x}{4 - x ^{4}} d x

\int_{0}^{\frac{3}{4}} x 9 - 4 x^{2} d x

\int_{0}^{2} x^{2} cos (nπ x) d x

What is the integral from-3 to 5 of [2y-(y^2-15)] ?
The integral from-3 to 5 of [2y-(y^2-15)] is 256/3