If f is continuous and integral from 0 to 10 of f(x) dx = 1, evaluate the integral from 0 to 2 of...

Question:

If {eq}f {/eq} is continuous and {eq}\int_{0}^{10} f(x) \, \mathrm{d}x = 1, {/eq} evaluate the integral {eq}\int_{0}^{2} f(5x) \, \mathrm{d}x {/eq}.

Definite Integral:

One of the properties of the definite integral is

{eq}\int_{a}^{b}f(x)dx=\int_{a}^{b}f(u)du {/eq}

Answer and Explanation:

{eq}\int_{0}^{10}f(x)dx=1\\ \int_{0}^{2}f(2x)dx\\ 2x=u\\ 2dx=du\\ \frac{1}{2}\int_{0}^{10}f(u)du\\ =0.5 {/eq}


Learn more about this topic:

Definite Integrals: Definition

from Math 104: Calculus

Chapter 10 / Lesson 6
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