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Popular >

integral from 1 to 3 of 1-x/3

Solution

\int_{1}^{3} 1 - \frac{x}{3} d x

Solution

\frac{2}{3}

+1

Decimal Notation

0.66666 \dots

Solution steps

\int_{1}^{3} 1 - \frac{x}{3} 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_{1}^{3} 1 d x - \int_{1}^{3} \frac{x}{3} d x

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

\int_{1}^{3} \frac{x}{3} d x = \frac{4}{3}

= 2 - \frac{4}{3}

Simplify

2 - \frac{4}{3} : \frac{2}{3}

= \frac{2}{3}

Popular Examples

integral from 6 to 10 of 0.5x^{-1.5}

\int_{6}^{10} 0.5 x^{- 1.5} d x

integral from 1 to 1 of ln(2x)

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

integral from 0 to x of 1/((1-x)^{0.4)}

\int_{0}^{x} \frac{1}{( 1 - x ) ^{0.4}} d x

integral from 1 to 2 of 3x+2

\int_{1}^{2} 3 x + 2 d x

integral from 1/2 to 1 of (ln(x))/(4x)

\int_{\frac{1}{2}}^{1} \frac{ln ( x )}{4 x} d x

Frequently Asked Questions (FAQ)

What is the integral from 1 to 3 of 1-x/3 ?
The integral from 1 to 3 of 1-x/3 is 2/3