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Popular >

integral from 0 to 6 of x(6-x)

Solution

\int_{0}^{6} x (6 - x) d x

Solution

36

Solution steps

\int_{0}^{6} x (6 - x) d x

Expand

x (6 - x) : 6 x - x^{2}

= \int_{0}^{6} 6 x - 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}^{6} 6 x d x - \int_{0}^{6} x^{2} d x

\int_{0}^{6} 6 x d x = 108

\int_{0}^{6} x^{2} d x = 72

= 108 - 72

Simplify

= 36

Popular Examples

integral from 1 to 5 of k(5-x)

\int_{1}^{5} k (5 - x) d x

integral from 0 to 2 of (x+1)^{2/3}

\int_{0}^{2} (x + 1)^{\frac{2}{3}} d x

integral from 2 to 4 of-4x^3ln(x)

\int_{2}^{4} - 4 x^{3} ln (x) d x

integral from 0 to sqrt(pi/2 of)sin(x^3)

\int_{0}^{\frac{π}{2}} sin (x^{3}) d x

integral from 1 to 4 of 2xsqrt(x^2+1)

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

Frequently Asked Questions (FAQ)

What is the integral from 0 to 6 of x(6-x) ?
The integral from 0 to 6 of x(6-x) is 36