Learn how to solve problems step by step online. Integrate the function 25^(-1)e^((-x)/25) from 1/30 to 1/20. Applying the property of exponents, \displaystyle a^{-n}=\frac{1}{a^n}, where n is a number. The integral of a constant times a function is equal to the constant multiplied by the integral of the function. We can solve the integral \int_{\frac{1}{30}}^{\frac{1}{20}} e^{\frac{-x}{25}}dx by applying integration by substitution method (also called U-Substitution). First, we must identify a section within the integral with a new variable (let's call it u), which when substituted makes the integral easier. We see that \frac{-x}{25} it's a good candidate for substitution. Let's define a variable u and assign it to the choosen part. Now, in order to rewrite dx in terms of du, we need to find the derivative of u. We need to calculate du, we can do that by finding the derivative of the equation above.

Integrate the function 25^(-1)e^((-x)/25) from 1/30 to 1/20