Final answer:
The question seems to be asking about calculating the r value for statistical correlation and integrating by parts, both of which are topics in college-level Mathematics. However, due to the lack of clear data points and a specific function to integrate, a precise answer cannot be provided.
Step-by-step explanation:
The information provided is insufficient and somewhat incoherent for a detailed answer. However, the mention of 'calculating the r value to indicate the correlation' falls under the subject of Mathematics, specifically in the area of statistics.
The r-value is a statistic that measures the strength and direction of a linear relationship between two variables on a scatterplot. The value of r is always between +1 and -1. To calculate it, you would typically need a set of paired data points and use the formula for the Pearson correlation coefficient.
In the case of integrating by parts, this is a technique used in calculus to find the integral of the product of two functions. The formula is generally given by ∫ u dv = uv - ∫ v du, where u and dv are chosen from the original integral so that du and v (the integral of dv) are simple to compute.