What is the integral from 2 to 4 of 1-(x-3)^2 ?

The integral from 2 to 4 of 1-(x-3)^2 is 4/3

Popular >

integral from 2 to 4 of 1-(x-3)^2

\int_{2}^{4} 1 - (x - 3)^{2} d x

\frac{4}{3}

Decimal Notation

1.33333 \dots

Solution steps

\int_{2}^{4} 1 - (x - 3)^{2} d x

Expand

1 - (x - 3)^{2} : - x^{2} + 6 x - 8

= \int_{2}^{4} - x^{2} + 6 x - 8 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} x^{2} d x + \int_{2}^{4} 6 x d x - \int_{2}^{4} 8 d x

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

\int_{2}^{4} 6 x d x = 36

\int_{2}^{4} 8 d x = 16

= - \frac{56}{3} + 36 - 16

Simplify

- \frac{56}{3} + 36 - 16 : \frac{4}{3}

= \frac{4}{3}

\frac{\partial}{\partial x} (6 q (r, t, x)^{2} + 7 r^{3} - \frac{8}{t} - q (r, t, x) t)

y y^{^{'}} + x = 0

x^{\frac{3}{4}}

\int y^{2} (1 - 2 x) d y

\frac{\partial}{\partial x} (y (e^{x} - 1))

What is the integral from 2 to 4 of 1-(x-3)^2 ?
The integral from 2 to 4 of 1-(x-3)^2 is 4/3