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Popular >

integral from 0 to 1 of x(4-x)

Solution

\int_{0}^{1} x (4 - x) d x

Solution

\frac{5}{3}

+1

Decimal

1.66666 \dots

Solution steps

\int_{0}^{1} x (4 - x) d x

Expand

x (4 - x) : 4 x - x^{2}

= \int_{0}^{1} 4 x - 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}^{1} 4 x d x - \int_{0}^{1} x^{2} d x

\int_{0}^{1} 4 x d x = 2

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

= 2 - \frac{1}{3}

Simplify

2 - \frac{1}{3} : \frac{5}{3}

= \frac{5}{3}

Graph

Popular Examples

integral from-1 to 2 of x^2+x+1

\int_{- 1}^{2} x^{2} + x + 1 d x

integral from 0 to 1 of tcosh(t)

\int_{0}^{1} t cosh (t) d t

integral from 0 to t^4 of sqrt(u^7)

\int_{0}^{t^{4}} u^{7} d u

integral from-1 to 0 of 4x(-4x^2+5)^3

\int_{- 1}^{0} 4 x (- 4 x^{2} + 5)^{3} d x

integral from 0 to 1 of k*(1-y)y^n

\int_{0}^{1} k \cdot (1 - y) y^{n} d y

Frequently Asked Questions (FAQ)

What is the integral from 0 to 1 of x(4-x) ?
The integral from 0 to 1 of x(4-x) is 5/3