Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
Chapter2: Graphical And Tabular Analysis
Section2.1: Tables And Trends
Problem 1TU: If a coffee filter is dropped, its velocity after t seconds is given by v(t)=4(10.0003t) feet per...
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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.
Question
![1. 6x-8)dx
Solve the following integrals as indicated. Observe neatness in showing your pertinent
solution.
Integration of Rational Factors,
2. (4y'-10y-18)dy
y-1)(y+1)(y+2)'
dz
3.
Integration by substitution
dy
4. -
y Jy-2ay
y'dy
5.
6. fx°cos x dx, Integration by parts
7. Find the area bounded by the curve y-3x + 2y-8 = 0 and the y - axis.
8. The area bounded the parabola y + x-2y = 2, the x- axis, and the line x = 3 revolves
about the line x 3. Find the volume.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F42b14db6-7693-40eb-a24b-0704fe164bfc%2Fec2805c4-4736-4c51-a983-ed166098c2e4%2Ftgk9d6y_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. 6x-8)dx
Solve the following integrals as indicated. Observe neatness in showing your pertinent
solution.
Integration of Rational Factors,
2. (4y'-10y-18)dy
y-1)(y+1)(y+2)'
dz
3.
Integration by substitution
dy
4. -
y Jy-2ay
y'dy
5.
6. fx°cos x dx, Integration by parts
7. Find the area bounded by the curve y-3x + 2y-8 = 0 and the y - axis.
8. The area bounded the parabola y + x-2y = 2, the x- axis, and the line x = 3 revolves
about the line x 3. Find the volume.
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