Step-by-step Solution

Integrate $\frac{8}{\sqrt{x}}$ from $3$ to $9$

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Step-by-step explanation

Problem to solve:

$\int_3^9\left(\frac{8}{\sqrt{x}}\right)dx$

Learn how to solve definite integrals problems step by step online.

$\int_{3}^{9}8x^{-\frac{1}{2}}dx$

Unlock this full step-by-step solution!

Learn how to solve definite integrals problems step by step online. Integrate 8/(x^0.5) from 3 to 9. Rewrite the exponent using the power rule \frac{a^m}{a^n}=a^{m-n}, where in this case m=0. The integral of a constant times a function is equal to the constant multiplied by the integral of the function. Apply the power rule for integration, \displaystyle\int x^n dx=\frac{x^{n+1}}{n+1}, where n represents a constant function, and equals -\frac{1}{2}. Evaluate the definite integral.

Final Answer

$20.2872$

Problem Analysis

$\int_3^9\left(\frac{8}{\sqrt{x}}\right)dx$

Main topic:

Definite integrals

Time to solve it:

~ 0.08 seconds