KTiaam said:Homework Statement
Evaluate the indefinite integral as an infinite series ∫ sin(x2) dx
Homework Equations
The Macluarin series of sin x =
∞
Ʃ (-1)nx2n+1/(2n+1)!
n=0
The Macluarin series for sin(x2) =
∞
Ʃ (-1)x4n+2/(2n+1)!
n=0
The Attempt at a Solution
Do i evaluate the integral of sin(x2)
from 0 to 1? then add the first couple of numbers to get a number or find a pattern?
An indefinite integral, also known as an antiderivative, is a mathematical concept used in calculus to find the original function when given its derivative. It represents the area under the curve of a function.
An infinite series is a sum of an infinite number of terms, with each term being calculated using a specific pattern or formula. It is a useful tool in mathematics for representing functions and solving problems.
To evaluate an indefinite integral as an infinite series, you must first find the indefinite integral of the given function. Then, you can use the formula for an infinite series to determine the value of the integral by taking the limit as the number of terms approaches infinity.
Evaluating an indefinite integral as an infinite series can help to solve complex problems that cannot be solved using other methods. It is also a useful tool for approximating values of integrals that cannot be solved analytically.
Yes, there are limitations to this method. It may not be possible to find an exact value for the integral if the series does not converge. Additionally, some functions may not have a known formula for their indefinite integral, making it impossible to evaluate as an infinite series.