If the substitution in the integration by trigonometric substitution is z = 3 tan 0, what would be the answer in the integral of the ending output is sec 0 - 0+ c? O Vz?+3 arctan + c 3 - arctan r +c 3 V49 - arctan +c 2243 arctan r c 3.

Q: You are working with your friends Alice and Bob on your Calculus homework. While you were away…

A: To tell if two different looking correct answers for the same integral is possible or not.

Q: Show that sin-1 v + cos-1 v = π/2 .

A: Given: sin-1 v+cos-1 v=π2

Q: What is csca if sec a = -4/3 and tana < 0?

A: What is csca if seca=-43 and tana&lt;0?

Q: The term 0.5(1-cos2x) is equal to

A: Given,          The term is 0.51-cos2x .

Q: Describe the technique for finding ∫ sec5 x tan7 x dx. Do not integrate.

A: Given ∫sec5x tan7x dx

Q: Make Detailed solution INTEGRATION OF TRIGONOMETRIC FUNCTIONS

A:

Q: 2. Is trigonometric substitution needed to evaluate /9 - x² dx?

A:

Q: O Find the anfidanialtiner Sfaw da for fla)= 18 Cos (6x) 16- Sin? (6x) © fa) = ¿* (, +x) 9 + xe

A:

Q: dx (5х+1)°

A:

Q: 6) sin e

A:

Q: sinx 0 cosx –sinx cosx is non singular for all values of x. 1 lect one:

A:

Q: Verify: 1. (sinx – cosx)² – 1 = -sin2x %3D

A: We can verify the statement as below

Q: Find |xV9x? +1 dx by using the trigonometric substitution of 3x = tan 0.

A:

Q: 18. sec(sin-1(x – 1)) (specify the domain)

A: Evaluate the function

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.