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.
Determine whether each
divergent. Evaluate those that are convergent.
∫-∞6 r er/3 dr
Given,
Now consider,
Use integration by parts rule,
Use the "LIATE" rule we get,
Now differentiate "u" we get,
And integrate "dv" we get,
Substitute the values in integrating by parts formula we get,
..(1)
Now consider,
+C
where C is the integral constant.
Now substitute the values in equation (1) we get,
Therefore,+C
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