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Popular >

integral from 2 to 4 of 16-x^2

Solution

\int_{2}^{4} 16 - x^{2} d x

Solution

\frac{40}{3}

+1

Decimal Notation

13.33333 \dots

Solution steps

\int_{2}^{4} 16 - 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_{2}^{4} 16 d x - \int_{2}^{4} x^{2} d x

\int_{2}^{4} 16 d x = 32

\int_{2}^{4} x^{2} d x = \frac{56}{3}

= 32 - \frac{56}{3}

Simplify

32 - \frac{56}{3} : \frac{40}{3}

= \frac{40}{3}

Popular Examples

integral from 1/2 to 4 of 1/(2x)

\int_{\frac{1}{2}}^{4} \frac{1}{2 x} d x

integral from 0 to pi/2 of sec(θ)

\int_{0}^{\frac{π}{2}} sec (θ) d θ

integral from 0 to pi of 3xcos(3x)

\int_{0}^{π} 3 x cos (3 x) d x

integral from 1 to infinity of 1/(2x+1)

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

integral from 3 to 2 of sin(x)

\int_{3}^{2} sin (x) d x

Frequently Asked Questions (FAQ)

What is the integral from 2 to 4 of 16-x^2 ?
The integral from 2 to 4 of 16-x^2 is 40/3