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Popular >

integral from 0 to x of 4-x^2

Solution

\int_{0}^{x} 4 - x^{2} d x

Solution

4 x - \frac{x ^{3}}{3}

Solution steps

\int_{0}^{x} 4 - 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_{0}^{x} 4 d x - \int_{0}^{x} x^{2} d x

\int_{0}^{x} 4 d x = 4 x

\int_{0}^{x} x^{2} d x = \frac{x ^{3}}{3}

= 4 x - \frac{x ^{3}}{3}

Popular Examples

integral from 0 to 24 of 8sqrt(t)

\int_{0}^{24} 8 t d t

integral from-pi to pi of sin^2(ax)

\int_{- π}^{π} sin^{2} (a x) d x

integral from 0 to 2 of 3x^2*sqrt(x^3+1)

\int_{0}^{2} 3 x^{2} \cdot x^{3} + 1 d x

integral from 10 to infinity of 2e^{-2x}

\int_{10}^{\infty} 2 e^{- 2 x} d x

integral from 0 to 1 of (3t^2-4t^3)

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

Frequently Asked Questions (FAQ)

What is the integral from 0 to x of 4-x^2 ?
The integral from 0 to x of 4-x^2 is 4x-(x^3)/3