Problem 13 The volume of the solid obtained by rotating the region bounded by x=(y^2), x=5y about the line y=5 can be computed using the method of washers or disks via an integral V=∫________________dx (with lower limit of a and upper limit of b) with limits of integration a=_________ and b=_________ The volume of this solid can also be computed using cylindrical shells via an integral V=∫_______________dy (with lower limt of alpha and upper limit of beta) with limits of integration alpha=_________ and beta=__________
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.
Problem 13
The volume of the solid obtained by rotating the region bounded by
x=(y^2), x=5y
about the line
y=5
can be computed using the method of washers or disks via an integral
V=∫________________dx
(with lower limit of a and upper limit of b)
with limits of
The volume of this solid can also be computed using cylindrical shells via an integral
V=∫_______________dy
(with lower limt of alpha and upper limit of beta)
with limits of integration alpha=_________ and beta=__________
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