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 Notation

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}

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

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

\int_{1}^{3} \frac{3 x - y}{9} d x

\int_{0}^{\frac{π}{2}} 4 d x

\int_{1}^{5} \frac{ln ( x ^{2} )}{x ^{3}} d x

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