What is the integral from-4 to-2 of (x^2+1/(x^3)) ?

The integral from-4 to-2 of (x^2+1/(x^3)) is 1783/96

Popular >

integral from-4 to-2 of (x^2+1/(x^3))

\int_{- 4}^{- 2} (x^{2} + \frac{1}{x ^{3}}) d x

\frac{1783}{96}

Decimal

18.57291 \dots

Solution steps

\int_{- 4}^{- 2} x^{2} + \frac{1}{x ^{3}} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{- 4}^{- 2} x^{2} d x + \int_{- 4}^{- 2} \frac{1}{x ^{3}} d x

\int_{- 4}^{- 2} x^{2} d x = \frac{56}{3}

\int_{- 4}^{- 2} \frac{1}{x ^{3}} d x = - \frac{3}{32}

= \frac{56}{3} - \frac{3}{32}

Simplify

\frac{56}{3} - \frac{3}{32} : \frac{1783}{96}

= \frac{1783}{96}

\int_{0}^{1} π (1 - x)^{2} d x

\int_{1}^{10} \frac{ln ^{3} ( x )}{x} d x

\int_{2}^{10} 2 x - 4 d x

\int_{- \infty}^{4} 2 e^{x} d x

\int_{2}^{4} \frac{x}{x ^{2} + 3 x + 2} d x

What is the integral from-4 to-2 of (x^2+1/(x^3)) ?
The integral from-4 to-2 of (x^2+1/(x^3)) is 1783/96