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- 6. Determine whether the integral is convergent or divergent. If it is convergent, evaluate it.∫ e^-1 dx Top is inf bottom is 1Mathematical Induction Use mathematical induction to verify that the following integral converges for any positive integer n? see the equation as attached hereThe integrals in Exercises converge. Evaluate the integrals without using tables
- Determine whether the integral is convergent or divergent. If it is convergent, evaluate it. (If the quantity diverges, enter DIVERGES.) The integral of [1/(5-x)^1/3]dx, from 0 to 5.The integral in this exercise converges. Evaluate the integral without using a table.Use the Series Integral test tol solve the following: Show it is positive, continuous, decreasing.
- Determine whether the integral is convergent or divergent. The integral from 6 to infinity, 1/(x-5)^3/2 dx If it is convergent, evaluate it. (If the quantity diverges, enter DIVERGES.Determine whether the integral is convergent or divergent. The integral from 0 to 11, 1/(11-x)^1/3 dx If it is convergent, evaluate it. (If the quantity diverges, enter DIVERGES.(a) Use any method to find the power series representation of f(x) =ln(x2)centered at 1. (b) Approximate the definite integral from 1 to 2, ln(x2)dx using a 2nd-order Taylor Polynomial for f(x) = ln(x2).
- Evaluate the indefinite integral as a power series. f(x)= integral of ln(1-t)/9tEvaluate the following integrals abd state if they converge or diverge. * The answer key sais the answer for this question is 2, but i need help understanding how to get to that conclusion.Determine whether the following integral converges or diverges. justify your answer