Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter8: Further Techniques And Applications Of Integration
Section8.2: Integration By Parts
Problem 34E
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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.
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![Evaluate the integral by making the given substitution. (Use C for the constant of integration.)
x2V x3 + 11 dx,
y = x3 + 11
u =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc8271c0e-0172-414d-940a-e4ac3aaae156%2F733b8ef3-8b66-4d6e-be8a-c81d65837b77%2Fckualse_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Evaluate the integral by making the given substitution. (Use C for the constant of integration.)
x2V x3 + 11 dx,
y = x3 + 11
u =
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