) Evaluate the definite integral. You may leave any irrational number (e, Ja, In(b), sin(c), ...) in answer. If the substitution method is used, state first u, du, ua, up and f flu)du. + sin(xx) – 2e3x )dx

Q: Evaluate the given definite integral: tan(x) dx A) In(3) 1 c) [In(2)]/2 In(2/3)

A:

Q: Evaluate the integral. Зл /2 7|sin æ| dæ

A: Consider the given integral

Q: 9. For the integral 8 sin" (x)cos(x)dx, if we use the substitution u = sin(x), what will be 3 the…

A: Topic - integration by substitution

Q: 12. Determine the definite integral 7 sint 0 cos3 0 de

A:

Q: Compute the indefinite integral. sin? COS T

A: YOUR ANSWER IS INCORRECT

Q: Evaluate the given definite integral: tan(x) dx = 1 B [In(2)]/2 In(2/3) In(3)

A: The objective of the question is evaluate the definite integral and choose the correct option.

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

A:

Q: Evaluate the definite integral. cos(T2) dz sin 8n Answer:

A: The given integral:∫08cosπxdxWe need to evaluate the above integral.

Q: Evaluate the integral. n/2 5 cos?0 de

A:

Q: Evaluate the integral sin? t cos t dt by making the substitution u = sin t. After substituting we…

A:

Q: The integral of (10*/ cos 10*)dx may be written as A In sec B* + tan B*|+ C. Where A, B, and C are…

A:

Q: 1 /- To evaluate the integral dx, using a trigonometric substitution, which substitution should you…

A: Evaluating integral by trignometric substitution

Q: To evaluate x² /1-x² dx using trigonometric substitution, what is the new integral in terms of 0 ? A…

A:

Q: The integral of (10*/cos 10*)dx may be written as A In sec B* + tan B* | + C. Where A, B, and C are…

A:

Q: 17. Use the theory of residue to evaluate the following definite integrals r2 (a) /" (b) / do 2+ cos…

A: 17(b) ∫02πcos2θ dθ5-4cosθ=real part of ∫02πei3θ dθ5-4cosθcosθ=real part of eiθsinθ=imaginary part of…

Q: 1+I dx Which one is the best substitution for evaluating the integral f cos Oz = u? Or = cos 20 I =…

A:

Q: 2- Solve the following integral with details 1 erlao cos? e r² dr sin@de ø do = x X = ? o 32ña

A: Given integral is  ∫02π∫0π∫0∞132πa05r3e-ra0cos2θ r2 dr sinθ dθ ϕ dϕ=x

Q: 8. Evaluate the integral: S 2r cos r dr

A: Given, ∫2r cos r dr We know that, ∫a fxdx=a∫ fxdx⇒2∫r cosr dr Now by using the Integration By Parts,…

Q: Use the value of the first integral I to evaluate the two given integrals.

A: Given: I=∫0π2cosθ-2sinθdθ=-1 we know that ∫abfxdx=-∫bafxdx

Q: Using substitution with u = sin(2x), the definite integral sin (2x) cos(2x) dx is equivalent to 1 1…

A:

Q: cos e d0 Jo 1+sin? A 2

A:

Q: Evaluate the integral by making exactly one u-substitution and applying any necessary formula(s)…

A:

Q: sin" zweos 2wdw

A:

Q: The integral of (10*/ cos 10*)dx may be written as A ln | sec B* + tan B* | + C. Where A, B, and C…

A:

Q: Evaluate the definite integral 2 (sin t, cos t) dt. COS 7/2 Select the correct anSwer helow:

A: We have to find out

Q: Suppose that a friend of yours has decided to solve a certain integral using trigonometric…

A:

Q: The integral of (10*/ cos 10*)dx may be written as A ln | sec B* + tan B* |+ C. Where A, B, and C…

A:

Q: ) Evaluate the definite integral. You may leave any irrational number (e, Ja, In(b), sin(c), ...) in…

A:

Q: 97. State whether the approximation MN or TN is larger or smaller than the integral. sin x dx 2л sin…

A:

Q: Rewrite the integral by substituting for cos 68. sin? 68 Vcos 68 sin 60 de du Apply the power rule…

A:

Q: sin 70 do 2+ cos 70 Evaluate the integral , using the substitution u = 2+ cos 70. sin 70 de 2 + cos…

A:

Q: Use integration by parts to prove the formula. ( assume that n is a positive integer.)

A: Consider the given integration as ∫eaxsinbxdx

Q: 7/2 S/² sin(x/2) cos(x/3) dx

A: This question is based on definite integral.

Q: (8) 20. Evaluate the following definite integrals: (a) (5 sin z + 7 cos(2r) + 3 sec² r) dr (b)

A:

Q: 22. Given that sinh 2 =, the value of cosh z is A. +- В. D. 4

A: Given: sinh x=34

Q: The integral of (10*/cos 10*)dx may be written as A In sec B* + tan B* | + C. Where A,„B, and C are…

A:

Q: Find the definite integral of: * 27 cos -w ) sin w) dw. O - 1/2 O - 1/12 О 12 2

A: The given integral is ∫π2π cos3w2 sin5w2 dw. Evaluate the above integral as follows.

Q: 12. By using the trigonometric substitution X = x = ; + sin(0) then the integral S - xp- (3+4x-4x2)…

A:

Q: 5. Calculate the integral sin"( t) cos*( t)dt. Your solution will be an expression in terms of m.…

A: To evaluate: I = ∫sinmtcos3tdt ⇒I = ∫sinmtcos2tcostdt⇒I = ∫sinmt1-sin2tcost dt

Q: Using substitution with u = sin(2x), the definite integral sin (2x) cos(2x) dx is equivalent to ...…

A: Use substitution

Q: 1/2 cos t Evaluate the integral o dt. 4.- sin? t In a Give your answer in the form where a and b are…

A: Given: ∫0π2cost4-sin2tdt Let sint=xcost=dx Then sin0=0sinπ2=1 So, ∫0π2cost4-sin2tdt=∫01dx4-x2

Q: Evaluate the integrals ∫ 1/cos 2θ sin θ dθ

A: Solution:- The given integral is  I=∫1cos2θsinθ dθ

Q: 4. Evaluate the following integral by trigonometric substitution [Apply the method that was taught…

A:

Q: 1 To evaluate the integral dx, using a trigonometric substitution, which x2 + 6x + 13 substitution…

A: Make the denominator in standard form than do the substitution such that integration become simpler.

Q: 2. The substitution u=cosx is suitable to solve the following integral: sin'x -dx cos 5x O False…

A: We have to check

Q: Evaluate integral S (2 sin a + 4 cos z) dæ

A:

Q: Evaluate the definite integral. •a / 4 2 + 5 cos?(0) de cos?(0)

A:

Q: 27n 4 cos x sin x dx 7/3

A:

Q: If you are going to evaluate the integral f cos x v9 + 25sin-x dx using trigonometric substitution,…

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.