This is not a precalculus question. You should post problems like this in the Calculus & Beyond section.WayneH said:Q: How many terms of the alternating series [tex]\sum((-2)^n)/n![/tex] needed to find the sum to an accuray of 0.01?
What approximations r going to help? I can not do with Riemann,Trapezoidal and Simpson.
An integral approximation is a method of estimating the value of a definite integral using numerical techniques. It involves dividing the integral into smaller parts and calculating the approximate area under the curve using these smaller parts.
Integral approximations are necessary because many integrals cannot be solved analytically. They are also useful for solving complex integrals that would otherwise be difficult or impossible to solve by hand.
Some common methods of integral approximation include the trapezoidal rule, Simpson's rule, and the midpoint rule. These methods use different techniques to divide the integral into smaller parts and calculate the approximate area under the curve.
The accuracy of an integral approximation depends on the method used and the number of subdivisions used to calculate the approximate area. Generally, the more subdivisions used, the more accurate the approximation will be.
No, integral approximations are most commonly used for definite integrals, where the limits of integration are known. They can also be used for some improper integrals, but may not be accurate in all cases. Additionally, integral approximations are not suitable for solving indefinite integrals.