Exercise
$\int_0^{15.5}\left(\frac{1}{768}\right)\cdot x^4\cdot e^{-\frac{x}{2}}dx$
Step-by-step Solution
Learn how to solve differential calculus problems step by step online. Integrate the function 1/768x^4e^((-x)/2) from 0 to 15.5. 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 x^4e^{\frac{-x}{2}}dx by applying the method of tabular integration by parts, which allows us to perform successive integrations by parts on integrals of the form \int P(x)T(x) dx. P(x) is typically a polynomial function and T(x) is a transcendent function such as \sin(x), \cos(x) and e^x. The first step is to choose functions P(x) and T(x). Derive P(x) until it becomes 0. Integrate T(x) as many times as we have had to derive P(x), so we must integrate e^{\frac{-x}{2}} a total of 5 times.
Integrate the function 1/768x^4e^((-x)/2) from 0 to 15.5
Final answer to the exercise
$1.3\times 10^{-3}\left(718.2750273-82646\cdot e^{-7.75}-5952\cdot e^{-7.75}-768\cdot e^{-7.75}\right)$