sinxdx if Which of the following integrals is obtained? X = Jó 1+cosx こ ド」N

Q: 8) Evaluate each of the integrals below by using antiderivatives. b) f, sin' xdx 3. a) sinx dx c)…

A: a)

Q: Write an equivalent integrals for the .function f(x,y)=4x+y for the following base (2,4) y= 2x y =…

A: Proceed as shown...

Q: Evaluate the following integrals i. SxIn(x+1)dx sin (Inx)cos (Inx), 2 ii.

A:

Q: 2. Use trigonometric substitution to find each of the following integrals. Don't forget to go back…

A:

Q: Which of the following integrals are improper? (Select all that apply.) dr 8r dr 2.x p sin (x) da…

A: First I have written a note, which tells about the improper integral , just use the definition of…

Q: Evaluate the following integral using trigonometric substitution. 5x? dx (81 + x)?

A:

Q: Evaluate the following integrals. 2 (a) S(csce)(1 + sin´e + sine cot + sin¯0 + sin0 cot¯0 ´e)de

A: Solution is given below:

Q: Evaluate the following integrals. 2. ∫[sin(ln?)+cos(ln?)]^2/? ??

A: Solving 2).

Q: Evaluate the multiple definite integral J, J. zr²sinu du dr dz

A:

Q: Evaluate the integral and interpret it as a difference ofareas. Illustrate with a sketch. ∫π/45π/2…

A:

Q: sech?x ix. xp: tanh(x)V1-tanh²x

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Use substitutions and the fact that a circle of radius r has an area πr^2 to evaluate the following…

A: ∫-π2π21-sin2x cosx dx Put, sinx=t⇒cosx=dtdx⇒cosx dx=dt When x=-π2, t=sin-π2=-1 When x=π2, t=sinπ2=1

Q: Evaluate the definite integral. 1 e? + 6 dz Jo ez + 6z

A:

Q: 4. S cot?x csc x dx

A: Note: As per company policy we are supposed to solve only 1 question. So, kindly repost other…

Q: Evaluate the following integral (b) / cosh" x sinh x dx (4 + sinh? x)²

A:

Q: Evaluate the following integrals: Given y = 3e* + 2 In 3x, is equal to? Solution:

A:

Q: {cot0P d® Q.4 Evaluate the following integral :

A:

Q: Decide whether the following integral is improper. 1 dx 3x -2 A) B) no yes

A: we will conclude the result.

Q: This triple integral can be broken into a product of integrals and evaluated, as follows. 27 (3r) dx…

A: Answer is 192π.

Q: Which one is a suitable substitution for the following integral? S -x²+4 x ○ x = 2 sec(t) O x = 4…

A: According to question,Given Integral,Let I = ∫-x2 + 4x dx

Q: state the trigon metri e subs tition you would use to Find the indefinite integral Do Not integrate.…

A:

Q: Evaluate the following integral and show your work: sin? x · cos? xdx ,2

A: Given :            ∫ sin2x cos2x dx

Q: 1. fese -Se- Side 2 f-ar +9' + de-de

A:

Q: Which of the following is the appropriate substitution to evaluate the given integral using…

A:

Q: Evaluate the integral frever se 2. 2. SS 24 S sinxy ds dx

A: According to the given information it is required to evaluate the given integral:

Q: Which of the following is the appropriate substitution to evaluate the given integral using…

A: This question is related to indefinite integration, we will solve it using given information.

Q: Evaluate the following integrals. 4 (a) (cot? 0 + csc? 0 sin 20) d0

A: definate integration

Q: S tan?xsec³x dx

A: To evaluate the following integral.∫tan2 x sec3 x dx

Q: Explain why each of the following integrals is improper  integral 0  to pie/4   cot x dx

A:

Q: Evaluate the integral and check your answer by differentiating. sec(x) + cos(x) dx 9 cos(x) + C

A: Formula : ∫sec2x=tanx+c

Q: +00 S" x?dx

A: To write that the given integral is improper or not.

Q: 8. State why the following integrals are improper, then evaluate each integral and state whether it…

A:

Q: 2. Evaluate the indefinite integral by trigonometric substitution ONLY. fr'VF+25dx

A:

Q: Evaluate the following integral using trigonometric substitution. dx xV4+x 13 증 2. 2.

A:

Q: Evaluate the f 2 3 8xy dxdy=? e following integral by usin tes -8 dA = ?

A: We have to find the value of the given integration according to the given information

Q: Which of the following integrals is equal to the integralf(3x- 5) dr? 7/3 (A f(2) dz dz 7/3 s(2) dz…

A: In this question we have to find the Integral which is equal to the given Integral. Given integral…

Q: Evaluate the following integrals.

A: Given: The integral ∫sinxcos2x+cosxdx To evaluate: The given integral.

Q: Which of the following integrals will represent the area outside r = 3, but inside r = 6 sin(0)?

A: area = 12∫ab[outer2 - inner2] dθ

Q: The integral of * x? dx is (x2+4)(x2+9) In(x? + 4) + In(x? + 9) + C Option 1 Option 2 -tan () + tan…

A: Given:     ∫x2dxx2+4x2+9 Perform partial fraction decomposition:     =∫95x2+9-45x2+4dx…

Q: L'²₁ (r + 1)² dr

A:

Q: csc x cot x dx

A:

Q: Which of the following integrals are improper? (Select all that apply.) 1 dr 6х — 1 1 dr 2.x – 1 sin…

A: We are asked to find which is improper integral

Q: (a) / Which of the following integrals is equal to -2+ In 2? X - 4 dx (a) 4- I dx (b) 2 - 4 da (c),…

A: To find which of the given integrals has given value

Q: Evaluate the integrals

A:

Q: Which of the following is the appropriate substitution to evaluate the given integral using…

A:

Q: When applying the u-substitution technique to this integral, we will need to exchange dx for du. 99…

A:

Q: Coso oxdox Sin?xcos? ad

A:

Q: Which of the following integrals are improper? Why?  integral 0 to pie / 4 tan x dx

A:

Q: Evaluate the improper integral or state that it is divergent. 1 dx x(x? + 3) 1 O A. In 4 In 4 OB.…

A:

Q: Evaluate the following integrals. 1. x sin r cos x dr.

A: topic - integration

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.