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Popular >

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

Solution

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

Solution

24

Solution steps

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

\int_{- 3}^{3} x^{2} d x = 18

\int_{- 3}^{3} x d x = 0

\int_{- 3}^{3} 1 d x = 6

= 18 + 0 + 6

Simplify

= 24

Popular Examples

integral from 0 to 2 of (x^6)/(1+x^2)

\int_{0}^{2} \frac{x ^{6}}{1 + x ^{2}} d x

integral from 0 to 1 of x/(2-x)

\int_{0}^{1} \frac{x}{2 - x} d x

integral from 0 to 2 of 2xln(1+x)

\int_{0}^{2} 2 x ln (1 + x) d x

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

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

integral from 1 to 3 of x^2+2x-5

\int_{1}^{3} x^{2} + 2 x - 5 d x

Frequently Asked Questions (FAQ)

What is the integral from-3 to 3 of (x^2+x+1) ?
The integral from-3 to 3 of (x^2+x+1) is 24