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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 2 to 4 of (m^2)/(m+1)

\int_{2}^{4} \frac{m ^{2}}{m + 1} d m

integral from-1 to 5 of 4x-x^2+5

\int_{- 1}^{5} 4 x - x^{2} + 5 d x

integral from 0 to pi of (x^2)cos(nx)

\int_{0}^{π} (x^{2}) cos (n x) d x

integral from 0 to t of cos(t^2)

\int_{0}^{t} cos (t^{2}) d t

integral from 1 to 12 of (1-x)(x-12)

\int_{1}^{12} (1 - x) (x - 12) 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