That substitution should work: show us what went wrong when you tried it.squenshl said:Homework Statement
How do I calculate ##\int_a^b x\left(\frac{b-x}{b-a}\right)^{n-1} \; dx##?
Homework Equations
The Attempt at a Solution
I tried the substitution ##u = \frac{b-x}{b-a}## to no avail. Someone please help.
Thanks a lot. I got it.Samy_A said:That substitution should work: show us what went wrong when you tried it.
A little hint: don't bother with the ##b-a## in the denominator, as that is a constant. Set ##u=b-x##.
EDIT: it doesn't really matter, both substitutions work just fine.
An integral is a mathematical concept that represents the accumulation of a quantity over a given interval. It is also known as the inverse operation of differentiation and is used to find the area under a curve on a graph.
To calculate this integral, you can use the power rule for integration, where you raise the power by 1 and divide the coefficient by the new power. In this case, you would raise the power of (b-x) to n and divide x by the new power.
The variables a and b represent the boundaries of the interval over which the integral is being calculated. a is the lower limit and b is the upper limit. These values define the range of values for which the accumulation is being calculated.
The exponent n represents the power to which the term (b-x) is being raised. This power helps determine the shape of the curve and the rate at which the quantity is being accumulated over the interval.
This type of integral can be used in various fields such as physics and economics to calculate the average value of a quantity over a given interval. For example, it can be used to calculate the average speed of a moving object over a certain time period or the average rate of change in stock prices over a specific time frame.