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Exercise

$\int_{\frac{1}{2}}^3\:\frac{\pi}{\left(x^2\right)}dx$

Step-by-step Solution

1

Rewrite the exponent using the power rule $\frac{a^m}{a^n}=a^{m-n}$, where in this case $m=0$

$\int_{\frac{1}{2}}^{3}\pi x^{-2}dx$
2

The integral of a constant times a function is equal to the constant multiplied by the integral of the function

$\pi \int_{\frac{1}{2}}^{3} x^{-2}dx$
3

Apply the power rule for integration, $\displaystyle\int x^n dx=\frac{x^{n+1}}{n+1}$, where $n$ represents a number or constant function, such as $-2$

$\pi \left[\frac{x^{-1}}{-1}\right]_{\frac{1}{2}}^{3}$
4

Simplify the expression

$\pi \left[\frac{1}{-x}\right]_{\frac{1}{2}}^{3}$
5

Evaluate the definite integral

$\pi \cdot \left(\frac{1}{- 3}- \frac{1}{- \frac{1}{2}}\right)$

Final answer to the exercise

$\pi \cdot \left(\frac{1}{- 3}- \frac{1}{- \frac{1}{2}}\right)$

Try other ways to solve this exercise

  • Choose an option
  • Integrate by partial fractions
  • Integrate by substitution
  • Integrate by parts
  • Integrate using tabular integration
  • Integrate by trigonometric substitution
  • Weierstrass Substitution
  • Integrate using trigonometric identities
  • Integrate using basic integrals
  • Product of Binomials with Common Term
  • Load more...
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$\int_0^{\infty}\left(\frac{1}{x^2}\right)dx$

$\int_0^1\left(\frac{3}{x^5}\right)dx$

$\int_1^{\infty}\left(\frac{1}{x^2}\right)dx$

Main Topic: Integrals of Polynomial Functions

Integrals of polynomial functions.

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