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Popular >

integral from 0 to x of (1-x)

Solution

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

Solution

x - \frac{x ^{2}}{2}

Solution steps

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

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

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

= x - \frac{x ^{2}}{2}

Popular Examples

integral from-0.5 to 7.6 of x^2+2x+1

\int_{- 0.5}^{7.6} x^{2} + 2 x + 1 d x

integral from 0 to 2 of (3x)/(x^2+4)

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

integral from 0 to pi/3 of 4sin(x)

\int_{0}^{\frac{π}{3}} 4 sin (x) d x

integral from 4 to 8 of (x^2)/2-2x+29

\int_{4}^{8} \frac{x ^{2}}{2} - 2 x + 29 d x

integral from 0.5 to 1 of 1/(x^2)

\int_{0.5}^{1} \frac{1}{x ^{2}} d x

Frequently Asked Questions (FAQ)

What is the integral from 0 to x of (1-x) ?
The integral from 0 to x of (1-x) is x-(x^2)/2