What is the integral from 60 to v of 1/(-0.4v^3) ?

The integral from 60 to v of 1/(-0.4v^3) is -2.5(-(0.5)/(v^2)+0.00013…)

Popular >

integral from 60 to v of 1/(-0.4v^3)

\int_{60}^{v} \frac{1}{- 0.4 v ^{3}} d v

- 2.5 (- \frac{0.5}{v ^{2}} + 0.00013 \dots)

Solution steps

\int_{60}^{v} \frac{1}{- 0.4 v ^{3}} d v

Take the constant out:

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

= \frac{1}{- 0.4} \cdot \int_{60}^{v} \frac{1}{v ^{3}} d v

Simplify

= (- 2.5) \cdot \int_{60}^{v} \frac{1}{v ^{3}} d v

Apply the Power Rule

: [- \frac{1}{2 v ^{2}}]_{60}^{v}

= (- 2.5) [- \frac{1}{2 v ^{2}}]_{60}^{v}

Simplify

= - 2.5 [- \frac{0.5}{v ^{2}}]_{60}^{v}

Compute the boundaries:

- \frac{0.5}{v ^{2}} + 0.00013 \dots

= - 2.5 (- \frac{0.5}{v ^{2}} + 0.00013 \dots)

\frac{( \frac{5}{s} - 1 )}{( s + 1 ) ^{2} + 9}

\int \frac{1}{1 + 6 x - 3 x ^{2}} d x

y^{^{'}} - 2 y = 3 e^{- 2 t}

\frac{d}{d x} (\frac{e ^{x^{2}}}{2})

(x + 1) \frac{d y}{d x} + (x + 2) y = 6 x e^{- x}

What is the integral from 60 to v of 1/(-0.4v^3) ?
The integral from 60 to v of 1/(-0.4v^3) is -2.5(-(0.5)/(v^2)+0.00013…)