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Popular >

integral from 0 to 4 of (4-x^2)

Solution

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

Solution

- \frac{16}{3}

+1

Decimal

- 5.33333 \dots

Solution steps

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

\int_{0}^{4} 4 d x = 16

\int_{0}^{4} x^{2} d x = \frac{64}{3}

= 16 - \frac{64}{3}

Simplify

16 - \frac{64}{3} : - \frac{16}{3}

= - \frac{16}{3}

Graph

Popular Examples

integral from 0 to t of e^x

\int_{0}^{t} e^{x} d x

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

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

integral from 3 to 4 of ln(x)

\int_{3}^{4} ln (x) d x

integral from 0 to 1 of xsqrt(x+1)

\int_{0}^{1} x x + 1 d x

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

\int_{0}^{x^{2}} 1 + t^{2} d t

Frequently Asked Questions (FAQ)

What is the integral from 0 to 4 of (4-x^2) ?
The integral from 0 to 4 of (4-x^2) is -16/3