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Popular >

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

Solution

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

Solution

3

Solution steps

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

Expand

(2 - x)^{2} : 4 - 4 x + x^{2}

= \int_{0}^{3} 4 - 4 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}^{3} 4 d x - \int_{0}^{3} 4 x d x + \int_{0}^{3} x^{2} d x

\int_{0}^{3} 4 d x = 12

\int_{0}^{3} 4 x d x = 18

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

= 12 - 18 + 9

Simplify

= 3

Popular Examples

integral from x^2 to x^3 of sin(x)

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

integral from 0 to ln(13) of tanh(x)

\int_{0}^{l n (13)} tanh (x) d x

integral from 0 to 2 of 1/(sqrt(y))

\int_{0}^{2} \frac{1}{y} d y

integral from 2 to 3 of 1/2

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

integral from 0 to 3pi of 1+cos(x)

\int_{0}^{3 π} 1 + cos (x) d x

Frequently Asked Questions (FAQ)

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