Riemann Sum
Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus.
Riemann Integral
Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.
Evaluate the integrals using
the given integral is:
we have to evaluate the integral using integration by parts.
lnx is the logarithmic function and is the algebraic function.
according to the ILATE rule where I stands for the inverse trigonometric functions, L stands for the logarithmic functions, A stands for the algebraic functions, T stands for the trigonometric functions and E stands for the exponential functions, the first function is lnx and the second function is .
and according to the integration by parts, we have:
where u is the first function and v is the second function.
therefore,
where C is the constant of integration.
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