Use a power series to approximate the value of the integral with an error of less than 0.0001. (Round your answer to four décimal place sin(x) dx

evaluate the definite integral.

A jungle has 400 monkeys, and it is estimated that the maximum population of the monkeys in the jungle is 10,000. The number of monkeys tripled in the first year. Write a differential equation that describes the population of monkeys in the jungle. Solve your differential equation to find the number of monkeys in the jungle as a function of time. When will the number of monkeys reach 5,000? When is the number of monkeys growing the fastest. Describe the method you used and show all work.

In the last part, wouldn't the range be calculated by the integral change due to the two substitutions to int from 0 to pi/3?

Evaluate by series approximation

a) Estimate the following definite integral numerically by using Simpson's rule. Take n=4 steps. [^²(x² + 1) dx -1

If V=R\power{3}, and W\index{1} is the xy plane and let W\index{2} is yz-plane:     W\index{1}={(x,y,0):x,y∈R}     W\index{2}={(0,y,z):y,z∈R} then V is not the direct sum of W\index{1} and W\index{2}.

Determine whether the integral is convergent or divergent. If it is convergent, evaluate it. (If the quantity diverges, enter DIVERGES.) *"e-1/x dx x2

Find integral 2  to 5    1/ sqrt  (x -2 ) dx