What is the integral from 3 to 4 of xsqrt(x-3) ?

The integral from 3 to 4 of xsqrt(x-3) is 12/5

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integral from 3 to 4 of xsqrt(x-3)

\int_{3}^{4} x x - 3 d x

\frac{12}{5}

Decimal

2.4

Solution steps

\int_{3}^{4} x x - 3 d x

Apply u-substitution

: \int_{0}^{1} (u + 3) u d u

= \int_{0}^{1} (u + 3) u d u

Expand

(u + 3) u : u^{\frac{3}{2}} + 3 u

= \int_{0}^{1} u^{\frac{3}{2}} + 3 u d u

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}^{1} u^{\frac{3}{2}} d u + \int_{0}^{1} 3 u d u

\int_{0}^{1} u^{\frac{3}{2}} d u = \frac{2}{5}

\int_{0}^{1} 3 u d u = 2

= \frac{2}{5} + 2

Simplify

\frac{2}{5} + 2 : \frac{12}{5}

= \frac{12}{5}

f (x) = \frac{1}{x + 9}, at x = - 7

\frac{\partial}{\partial x} (3 y e^{4 x y} + 8 x)

\int \frac{3}{12 x - 1} d x

f (x) = \frac{x}{e ^{x}}

\frac{\partial}{\partial x} (x^{2} - x y + 8 y^{2})

What is the integral from 3 to 4 of xsqrt(x-3) ?
The integral from 3 to 4 of xsqrt(x-3) is 12/5