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Popular >

integral from 0 to 2 of 16x-x^5

Solution

\int_{0}^{2} 16 x - x^{5} d x

Solution

\frac{64}{3}

+1

Decimal Notation

21.33333 \dots

Solution steps

\int_{0}^{2} 16 x - x^{5} 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}^{2} 16 x d x - \int_{0}^{2} x^{5} d x

\int_{0}^{2} 16 x d x = 32

\int_{0}^{2} x^{5} d x = \frac{32}{3}

= 32 - \frac{32}{3}

Simplify

32 - \frac{32}{3} : \frac{64}{3}

= \frac{64}{3}

Popular Examples

integral from 1 to 2 of 3/7 x^2x^2

\int_{1}^{2} \frac{3}{7} x^{2} x^{2} d x

integral from 2 to 4 of sqrt(3+x^2)

\int_{2}^{4} 3 + x^{2} d x

integral from 0 to pi of sin(2x)cos(nx)

\int_{0}^{π} sin (2 x) cos (n x) d x

integral from 2 to 6 of 6x^2ln(3x)

\int_{2}^{6} 6 x^{2} ln (3 x) d x

integral from 0 to pi/4 of 4sec(x)tan(x)

\int_{0}^{\frac{π}{4}} 4 sec (x) tan (x) d x

Frequently Asked Questions (FAQ)

What is the integral from 0 to 2 of 16x-x^5 ?
The integral from 0 to 2 of 16x-x^5 is 64/3