1. For each of the following integrals, think about what by-hand method (substitution, parts, powers oftrig functions, or some combination) is most likely to work. What should you do first? What do youexpect to see when you're done?. fx In(3x)dx| sin xVcos xdxb.4x3-dx| csc* xcot x dxC.Vx* +9d..fx*(In x)² dx| cos? x sin? xdxf.е.(You do not have to actually do the integrations. But you may integrate these for practice. I'll postanswers on Canvas later.)2. Here is an integral that can be done in many different ways, using techniques we have learned in thisclass combined with possible clever algebra.1Evaluatex7-xThe object here is to find as many different ways to integrate this as possible.

1. For each of the following integrals, think about what by-hand method (substitution, parts, powers o trig functions, or some combination) is most likely to work. What should you do first? What do you expect to see when you're done? (x In(3x)dx | sin xVcos xdx а. b. 4x3 csc* xcot x d d. csc*, Vx* +9

1. For each of the following integrals, think about what by-hand method (substitution, parts, powers o trig functions, or some combination) is most likely to work. What should you do first? What do you expect to see when you're done? (x In(3x)dx | sin xVcos xdx а. b. 4x3 csc* xcot x d d. csc, Vx +9

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Concept explainers

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

100%

1. For each of the following integrals, think about what by-hand method (substitution, parts, powers of
trig functions, or some combination) is most likely to work. What should you do first? What do you
expect to see when you're done?
. fx In(3x)dx
| sin xVcos xdx
b.
4x3
-dx
| csc* xcot x dx
C.
Vx* +9
d.
.fx*(In x)² dx
| cos? x sin? xdx
f.
е.
(You do not have to actually do the integrations. But you may integrate these for practice. I'll post
answers on Canvas later.)
2. Here is an integral that can be done in many different ways, using techniques we have learned in this
class combined with possible clever algebra.
1
Evaluate
x7-x
The object here is to find as many different ways to integrate this as possible.

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