What is the integral from 2 to 3 of tsqrt(t-2) ?

The integral from 2 to 3 of tsqrt(t-2) is 26/15

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integral from 2 to 3 of tsqrt(t-2)

\int_{2}^{3} t t - 2 d t

\frac{26}{15}

Decimal Notation

1.73333 \dots

Solution steps

\int_{2}^{3} t t - 2 d t

Apply u-substitution

: \int_{0}^{1} (u + 2) u d u

= \int_{0}^{1} (u + 2) u d u

Expand

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

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

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

\int_{0}^{1} 2 u d u = \frac{4}{3}

= \frac{2}{5} + \frac{4}{3}

Simplify

\frac{2}{5} + \frac{4}{3} : \frac{26}{15}

= \frac{26}{15}

\frac{d}{d j} (3 i - 5 j)

\int \frac{1}{cos ( t )} d t

y = 6, y = x^{- 2} + x^{2}

\int e^{(3 - x)} d x

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

What is the integral from 2 to 3 of tsqrt(t-2) ?
The integral from 2 to 3 of tsqrt(t-2) is 26/15