What is the integral from 2 to 2x of sqrt(15-t) ?

The integral from 2 to 2x of sqrt(15-t) is -(2(15-2x)^{3/2}-26sqrt(13))/3

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integral from 2 to 2x of sqrt(15-t)

\int_{2}^{2 x} 15 - t d t

- \frac{2 ( 15 - 2 x ) ^{\frac{3}{2}} - 26 13}{3}

Solution steps

\int_{2}^{2 x} 15 - t d t

Apply u-substitution

: \int_{13}^{15 - 2 x} - u d u

= \int_{13}^{15 - 2 x} - u d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - \int_{13}^{15 - 2 x} u d u

Apply the Power Rule

: [\frac{2}{3} u^{\frac{3}{2}}]_{13}^{15 - 2 x}

= - [\frac{2}{3} u^{\frac{3}{2}}]_{13}^{15 - 2 x}

Compute the boundaries:

\frac{2}{3} (15 - 2 x)^{\frac{3}{2}} - \frac{26 13}{3}

= - (\frac{2}{3} (15 - 2 x)^{\frac{3}{2}} - \frac{26 13}{3})

Simplify

= - \frac{2 ( 15 - 2 x ) ^{\frac{3}{2}} - 26 13}{3}

y = x^{5} cos (x)

\frac{d}{d x} (a (x + 1) (x - r))

t y^{^{'}} + y = 0

\frac{d x}{d t} = x - 4

\int_{1}^{\infty} \frac{x}{x ^{4} + 1} d x

What is the integral from 2 to 2x of sqrt(15-t) ?
The integral from 2 to 2x of sqrt(15-t) is -(2(15-2x)^{3/2}-26sqrt(13))/3