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Popular >

integral from 3 to-3 of 9-x^2

Solution

\int_{3}^{- 3} 9 - x^{2} d x

Solution

- 36

Solution steps

\int_{3}^{- 3} 9 - x^{2} d x

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{- 3}^{3} 9 - 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_{- 3}^{3} 9 d x - \int_{- 3}^{3} x^{2} d x)

\int_{- 3}^{3} 9 d x = 54

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

= - (54 - 18)

Simplify

= - 36

Popular Examples

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

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

integral from 0 to 4 of ysqrt(9+y^2)

\int_{0}^{4} y 9 + y^{2} d y

integral from 0 to 1 of (x^{4/3}-2x^{1/3})

\int_{0}^{1} (x^{\frac{4}{3}} - 2 x^{\frac{1}{3}}) d x

integral from 1 to 6 of |4x-12|

\int_{1}^{6} ∣ 4 x - 12 ∣ d x

integral from 0 to 1 of (1-2x)^3

\int_{0}^{1} (1 - 2 x)^{3} d x

Frequently Asked Questions (FAQ)

What is the integral from 3 to-3 of 9-x^2 ?
The integral from 3 to-3 of 9-x^2 is -36