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Popular >

integral from-1 to 3 of (2x-x^2)

Solution

\int_{- 1}^{3} (2 x - x^{2}) d x

Solution

- \frac{4}{3}

+1

Decimal Notation

- 1.33333 \dots

Solution steps

\int_{- 1}^{3} 2 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_{- 1}^{3} 2 x d x - \int_{- 1}^{3} x^{2} d x

\int_{- 1}^{3} 2 x d x = 8

\int_{- 1}^{3} x^{2} d x = \frac{28}{3}

= 8 - \frac{28}{3}

Simplify

8 - \frac{28}{3} : - \frac{4}{3}

= - \frac{4}{3}

Popular Examples

integral from 1 to 2 of xe^{-x^2+1}

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

integral from 0 to pi/2 of (sin(2t))

\int_{0}^{\frac{π}{2}} (sin (2 t)) d t

integral from 0 to 1 of sqrt(4x+3)

\int_{0}^{1} 4 x + 3 d x

integral from 2 to 4 of x/((x^2+1)^3)

\int_{2}^{4} \frac{x}{( x ^{2} + 1 ) ^{3}} d x

integral from 0 to pi/4 of (2sec^2(x))

\int_{0}^{\frac{π}{4}} (2 sec^{2} (x)) d x

Frequently Asked Questions (FAQ)

What is the integral from-1 to 3 of (2x-x^2) ?
The integral from-1 to 3 of (2x-x^2) is -4/3