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Popular >

integral from 0 to 3 of |4-x^2|

Solution

\int_{0}^{3} 4 - x^{2} d x

Solution

\frac{23}{3}

+1

Decimal Notation

7.66666 \dots

Solution steps

\int_{0}^{3} 4 - x^{2} d x

Eliminate Absolutes

= \int_{0}^{2} 4 - x^{2} d x + \int_{2}^{3} - 4 + x^{2} d x

\int_{0}^{2} 4 - x^{2} d x = \frac{16}{3}

\int_{2}^{3} - 4 + x^{2} d x = \frac{7}{3}

= \frac{16}{3} + \frac{7}{3}

Simplify

\frac{16}{3} + \frac{7}{3} : \frac{23}{3}

= \frac{23}{3}

Popular Examples

integral from e to 1 of sqrt(t)ln(t)

\int_{e}^{1} t ln (t) d t

integral from x to a of 2^{ln(t)}

\int_{x}^{a} 2^{l n (t)} d t

integral from 0 to 1 of (e^x)^3

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

integral from-2 to-1 of (2x-1)e^{2x}

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

integral from 4 to 7 of 1/(4x^2-8x-5)

\int_{4}^{7} \frac{1}{4 x ^{2} - 8 x - 5} d x

Frequently Asked Questions (FAQ)

What is the integral from 0 to 3 of |4-x^2| ?
The integral from 0 to 3 of |4-x^2| is 23/3