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Popular >

integral from 0 to 3 of x(x-2k)

Solution

\int_{0}^{3} x (x - 2 k) d x

Solution

9 - 9 k

Solution steps

\int_{0}^{3} x (x - 2 k) d x

Expand

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

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

\int_{0}^{3} x^{2} d x = 9

\int_{0}^{3} 2 k x d x = 9 k

= 9 - 9 k

Popular Examples

integral from 0 to 2 of x(x/2)

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

integral from 1 to 5 of 2/t

\int_{1}^{5} \frac{2}{t} d t

integral from-a to a of |a+3t|

\int_{- a}^{a} ∣ a + 3 t ∣ d t

integral from 0 to 2 of r

\int_{0}^{2} r d r

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

\int_{0}^{3} π (x^{2})^{2} d x

Frequently Asked Questions (FAQ)

What is the integral from 0 to 3 of x(x-2k) ?
The integral from 0 to 3 of x(x-2k) is 9-9k