2. (a) Determine whether the integral given is proper or improper(if so, explain why). 1 dx – 1| Hence evaluate the integral. (b) Use the comparison test to determine whether or not the integral +00 1 dx x4 + ex converges.
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.
(a) Determine whether the
\int _0^2\:\frac{1}{\left|x-1\right|}dx
Hence evaluate the integral.
(b) Use the comparison test ppto determine whether or not the integral
\int _1^{+\infty }\:\frac{1}{^{^{x^4+e^x}}}dx
converges.
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