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Popular >

integral from 0 to 1 of 6x-x^2

Solution

\int_{0}^{1} 6 x - x^{2} d x

Solution

\frac{8}{3}

+1

Decimal Notation

2.66666 \dots

Solution steps

\int_{0}^{1} 6 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} 6 x d x - \int_{0}^{1} x^{2} d x

\int_{0}^{1} 6 x d x = 3

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

= 3 - \frac{1}{3}

Simplify

3 - \frac{1}{3} : \frac{8}{3}

= \frac{8}{3}

Popular Examples

integral from 0 to 2 of ysqrt(x+2)

\int_{0}^{2} y x + 2 d x

integral from 0 to 4 of (x/(1+x^4))

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

integral from 0 to 2 of x/((x-1)^2(x+1))

\int_{0}^{2} \frac{x}{( x - 1 ) ^{2} ( x + 1 )} d x

integral from 0 to 1 of sin(y^2)y

\int_{0}^{1} sin (y^{2}) y d y

integral from o to t of t

\int_{o}^{t} t d t

Frequently Asked Questions (FAQ)

What is the integral from 0 to 1 of 6x-x^2 ?
The integral from 0 to 1 of 6x-x^2 is 8/3