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Popular >

integral from 0 to 3 of x(x+1)

Solution

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

Solution

\frac{27}{2}

+1

Decimal Notation

13.5

Solution steps

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

Expand

x (x + 1) : x^{2} + x

= \int_{0}^{3} x^{2} + x 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}^{3} x^{2} d x + \int_{0}^{3} x d x

\int_{0}^{3} x^{2} d x = 9

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

= 9 + \frac{9}{2}

Simplify

9 + \frac{9}{2} : \frac{27}{2}

= \frac{27}{2}

Popular Examples

integral of sqrt(4-9z^2)

\int 4 - 9 z^{2}

(d^2)/(dx^2)(2e^{4x})

\frac{d ^{2}}{d x ^{2}} (2 e^{4 x})

laplacetransform (t+1)^3 laplace transform

(t + 1)^{3}

derivative of sqrt(3-x)derivative of

3 - x

(\partial)/(\partial x)(-4+2e^x-3)

\frac{\partial}{\partial x} (- 4 + 2 e^{x} - 3)

Frequently Asked Questions (FAQ)

What is the integral from 0 to 3 of x(x+1) ?
The integral from 0 to 3 of x(x+1) is 27/2