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Popular >

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

Solution

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

Solution

\frac{8}{3}

+1

Decimal

2.66666 \dots

Solution steps

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

\int_{- 1}^{3} 3 x d x = 12

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

= 12 - \frac{28}{3}

Simplify

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

= \frac{8}{3}

Graph

Popular Examples

integral from 0 to pi/2 of cos^2(3t)

\int_{0}^{\frac{π}{2}} cos^{2} (3 t) d t

integral from 0 to pi/4 of (8sec^2(x))

\int_{0}^{\frac{π}{4}} (8 sec^{2} (x)) d x

integral from 1 to 2 of (15x^4-4x)

\int_{1}^{2} (15 x^{4} - 4 x) d x

integral from 1 to 2 of (8x^3+6/(x^2))

\int_{1}^{2} (8 x^{3} + \frac{6}{x ^{2}}) d x

integral from 0 to 2 of (6-x-y)/8

\int_{0}^{2} \frac{6 - x - y}{8} d x

Frequently Asked Questions (FAQ)

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