3. Consider the integral / sin x dx. (a) Evaluate the integral by an appropriate reduction formula in Section 8.1, and write the constant added at the end as C1. (b) Evaluate the integral by the method of Section 8.2 (i.e., by factoring out sin x and by writing the rest of the integrand in terms of cos x), and write the constant added at the end as C2. (c) Show that the results found in (a) and (b) are compatible, by finding a relationship between C1 and C2. (Hint: Eliminate sinx from the answers in (a) and/or (b).)

Q: 5) find the integral J8 sin 2x * cos2x dx

A: see below the calculation and answer

Q: Evaluate the integral. Зп /4 6 sin (x) cos (x) dx Jn/2

A:

Q: The suitable substitution to evaluate the integral tan (2x) dx is 4 C cos“(2x)

A: Explanation: Given that, ∫tan52xcos42xdx

Q: 18 Estimate the error if cos t is approximated by 1- 2 in the integral cos t? dt. 4! - -+ The error…

A:

Q: 4. Evaluate the integral. S tan (2x) sec°(2x) dx

A:

Q: S sin x In(cosx) dx

A: To evaluate the integral: I=∫sin x(ln (cos x)) dx Substitute  cos x=t⇒-sin x dx=dt⇒sin x dx=-dt

Q: Use the substitution formula to evaluate the integrals ∫ pi over 4 at the top and 0 at the bottom…

A:

Q: . Find the integral [cos (3x - 2)dx

A: A detailed solution is given below.

Q: Evaluate the integral: 25 tan² 12x dx Choose the most appropriate answer. tan3 3 12x O 25 × 1 12 ln…

A: Explanation of the answer is as follows

Q: 17. Why doesn't the definite integral 1-x² dx make sense? (Hint: Think about domains.)

A: To find: The reason why the definite integral ∫231-x2dx does not make sense. Explanation: Substitute…

Q: The undefined integral of the function [x. (x - 2)] power -1 is * O sin [ exp (x-2/x) power 0.5] + c…

A: We will find the undefined  integral as following.

Q: Evaluate the integral. S-3x cos(2x) dx

A:

Q: Find integral of sin^2 (x/2) dx with bounds of 0 to pi

A: Find the integral of sin^2 (x/2) dx with the bounds 0 to π.

Q: evaluate the integral

A:

Q: Express lim,00 E= cos( + ) in integral notation. i=1 _2n

A: Since, the above equation is given in the form of Riemann's integral, which is given by-…

Q: Which of the following is equal to sec 2x tan³x dx to obtain the correct indefinite integral? A x-…

A: The given integral,        ∫sec32x tan3x dx

Q: 2. Use reduction formula to evaluate the integral: sin xdx.

A: We have to evaluate integral by using reduction formula.

Q: 3 Which of the following is equal to / sec 2 x tan³x dx to obtain the correct indefinite integral? A…

A:

Q: Evaluate the integral 1—е-4а sin x cos 3xdx

A:

Q: 3 4. sin x cos xdx

A: These formulae are used while solving the question:

Q: Find the integral of 12 sin^5 x cos^5 x dx if the lower limit is O and the upper limit is T/2.

A:

Q: Evaluate the integral. ∫ Cos2 x Sin2x dx

A: Given :           ∫cos2x sin2x dx

Q: Evaluate the integral. 7- sin 6x dx 6 7n 1 7n 1 18

A:

Q: 1. Evaluate the integral using FTC Part 1. | (23 – 2a) dæ 2. Evaluate the integral using FTC Part 2.…

A: As per guideline we have to solve only one question

Q: Obtain a formula that expresses the integral [cos". cos" x dx

A:

Q: x² /16 – x²dx

A:

Q: Find the definite integral of ƒ™/* cos 3x sin 5x dx. -π/4 Option 1: Option 2: Option 3: Option 4:…

A:

Q: Question 1 Evaluate the following integrals using residue theorem: Lx (2² + 9) (2² + (b) 2³ sin uz…

A:

Q: 8 (a) To evaluate the integral J cos xdx by using the reduction formula of Cosine function.

A: We have to use cosine reduction formula.

Q: (a) Evaluate the integral sin* 4x cos3 4x dx

A: a) Evaluate the integral                                 ∫0π8 sin4 4x cos3 4x dx  Let us substitute…

Q: Which of the following is one of the correct steps to evaluate cos3 dt to obtain the correct indef…

A:

Q: , 1. Take the following integral numerically using an end corrected method. (n-7, h=0.001) (give…

A:

Q: - Evaluate the integral: S cos3x/sinx dx.

A: Explanation: Given that: ∫cos3xsinxdx Concept used: 1. sin2x+cos2x=12.∫xndx           =xn+1n+1+C 3.…

Q: 6. Evaluate the fallowing real integrals by residue. theerem 3 -bm -am 응) Co3 mX ans : X Sin mx ans…

A:

Q: Solve the integral. cos x dx J (1+ sin² x) arctan (sin x) 10.

A: To evaluate:                      ∫cos x(1+sin2 x)arctan(sin x)dx    ... (1)

Q: 5. Evaluate the following indefinite integrals. 8. **** Power 2 ...... sin.x dx. b-₁f.co₂x² dx…

A:

Q: 5. Express the integral: e- dr in terms of gamma function.

A:

Q: the integral of tan^2 (x) cos^3 (x)dx

A: To evaluate the given trigonometric integral

Q: Evaluate the integrals

A: Our Aim is to evaluate the integral given below:-∫-π3π3 sin2(t) dt.

Q: Find the integral cos 10 using the substitution u = Enclose arguments of functions in parentheses.…

A: Explanation of the solution is given below...

Q: Evaluate the integral.  integral sin 3  x cos 2 x dx

A:

Q: Evaluate the following integral in image 20200523_215458.jpg (b)Find the equation of the tangent to…

A:

Q: Q5. Approximate the integral Sin(2x)dx (i) Using composite Sympson's rule with n = 2,4 and

A: As per the policy of bartleby the provisions is to solve only one question at a time so I am solving…

Q: 25. f(x) = {1 0<x< 0, sx<1

A:

Q: 3- Evaluate the integral sin(In x)dx

A: We have to use integration by parts 2 times here.

Q: 2 sin6 x cos⁹ x dx 0

A: See the details solution in below

Q: b) Evaluate the integral: S (sin-1(x))²dx

A:

Q: Evaluate the integral.  integral cos  - 4  x  dx

A:

Q: Evaluate the integral. 6 sin -1 x dx

A: Given problem:- ∫ 6sin-1(x) dx

Q: 5. Calculate the integral f sin"( 1) cos'( t) dt, Your solution will be an expression in terms of m.…

A:

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.