Transform the integral 7 n do d0 by the substitution r = sin o cos 0, y = sin ø sin 0 and then sin 6 find its value.

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

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

A: Consider the given integral

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Q: The resulting integral of sin -cos- sino do has the form --F(0)+C. What should be the value of e to…

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Q: Evaluate the integral. 1/2 Jo 7 cos-¹(x) dx

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

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

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Q: Evaluate the integral sin^4 e de from 0 to π/2 * 2π/3 TT/4 31/16 31/5 O h

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Q: Evaluate the integral 1 dx |(1+ sin æ)² Hint: Multiply the numerator and denominator by (1 – sin…

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Q: Evaluate the integral. a) 8. da x4 b) | (tan(5a)+ sec(5x)) dx | 8sin(2) cos(x) dæ

A: Given integral are a)   ∫x38-x4dxb)    ∫(tan(5x)+sec(5x))dxc)∫8sinxCosx dx we can evaluate these…

Q: evaluate the integral

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Q: 2n do 3 + sin 0 + cos 0

A: Given integral is ∫02πdθ3+sinθ+cosθ Given z=eiθ We know that  eiθ=cosθ+isinθ e-iθ=cosθ-isinθ So…

Q: Find the integral SPos (*) dt using the substitution u = t4. Enclose arguments of functions in…

A: Given I=∫ t3 cos t4 dt -1

Q: Evaluate the definite integral by expressing it in terms of u and evaluating the resulting integral…

A: We have to find out the integration of above trignometric function

Q: sin 40 do 9 + cos 40 Evaluate the integral ; using the substitution u = 9+ cos 40. sin 40 do 9+ cos…

A: ∫sin4θ9+cos4θ dθ

Q: Find the integral t sin(6t) dt. NOTE: Enclose arguments of functions in parentheses. For example,…

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Q: Find the integral t5 cos |dt using the substitution u = t6. Enclose arguments of functions in…

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Q: the ng tan (3r) sec" (3r) dx. (i) By using the substitution u = 3a, transform the original integral…

A: The solution follows as:

Q: Write the integral in terms of u and du. Then evaluate. sin (20 – 6) de, u = 20 – 6 (Use symbolic…

A: The given integral is ∫sin2θ-6dθ. To evaluate the value of given integral substitute u for 2θ-6.

Q: Evaluate the integral. 8 sin x dx + C NOTE: Enter the exact answer in expanded form.

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Q: Evaluate the integral. 6 sin" -1 dx: +C |3D NOTE: Enter the exact answer in expanded form.

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

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Q: Evaluate the integral. 2 sin ] x dx + C NOTE: Enter the exact answer in expanded form.

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Q: Evaluate the integral. 2 sin x dx + C NOTE: Enter the exact answer in expanded form.

A: I=∫2sin-1xdx

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

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Q: Consider the integral / sin*+1x - cos x dx , where k is a positive integer. Using the methods…

A: By using u substitution method

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

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Q: Evaluate the integral ² ² sin² 20 r dr de where D = {(r, 0)| 0 ≤ 0 ≤ñ, 0≤ r ≤ 2√cos 20}. X

A: Solution: ∫∫Dr2sin2(2θ)rdrdθθ→0 to πr→0 to 2cos 2θ

Q: Transform the integral fo So? sin o sin 0 do do by the substitution r = sin o cos 0, y = sin o sin 0…

A: Given ∫0π2∫0π2sinϕsinθdϕdθand x=sinϕcosθ, y=sinϕsinθ

Q: Evaluate the integral. S O sin.c tan 5 dx 49 – 25x² Sin-1 + C + C O tan-1 + C sin-1 + C

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Q: 6. [t cos"(7*) dr

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

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Q: Evaluate the integral. 28) sin dt A) -cos B) cos C) 5 cos + 6 D) COS 1/5 +

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

Q: S The integral S x dx x²+√√x²-1-1 sece tane de sece - 1 sec²0 do 1+tano cose dᎾ 1 - sino sine de 1 +…

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Q: Find the integral 10 sin (t11 ) dt using the substitution u = t11 Enclose arguments of functions in…

A: The given integral is,

Q: Consider the integral cos“ x · sin'x dx , where k is a positive cos“ x• integer. Using the methods…

A: ∫coskx . sin3x dx∫coskx . sin2x .  sinx dx∫coskx . (1-cos2x) .  sinx dx               ( sin2x =…

Q: Evaluate the definite integral. 7/3 /3 " sec(t)( tan(t) + sec(t) dt = Hint: First multiply out the…

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Q: Given SV-x* + 4x + 5 dx. Using trigonometric substitution, what is the integral form in terms of 8?…

A: Trigonometric identities: sin2θ+cos2θ=1cos2θ=1+cos2θ2 If an expression is x2+bx, then we need to add…

Q: Evaluate the integral: sin 0 So S 0 dr do. So Soin e dr de = 1 So Lsin 0 dr d0 = -5 So Ssin 0 dr de…

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Q: x = 9 tan 0 is an appropriate trigonometric substitution for the integral Select one: O True O False…

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

A: Given that: ∫cos8(9x).sin(9x)dx

Q: Use the convolution theorem to evaluate the integral. sin(2 · 7) cos((t – T))dr COS

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Q: Evaluating the integral (cos x- 2sin x)dx gives: А. -2 В.О С. 1 D. -4

A: Option D is correct Explanation is given below

Q: Match the integral expression on the left to an equal expression on the right. Prompts Submitted…

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Q: The substitution 2=tan 2 transformed the integral dx Stadz, expression 5sin(x) – 12cos(x) + 13 into…

A: Consider the given integral ∫dx5sinx-12cosx+13 Take the substitution z=tanx2 to transform the given…

Q: To evaluate the integral 4+2a dr, we use Select one: O Substitution with a = 2 sin 0, where…

A: Given :∫4+x2dx

Q: Evaluate the integral using the given substitution. sin- dx Select one: A.-1 +1 sin2 + C x 2 3 B.-1…

A: Given information:-

Q: Evaluate the integral 2 S 35 sin 4x cos 3xdx 3x/2 2 35 sin xcos 3x dx 3/2 (Simplify your answer,…

A: Evaluate the given definite integral as follows.

Q: Evaluate the integral: 30dx / (1-cos(5x)) The solution to the integral is -6(Cot(5x) + Csc(5x)) + C…

A: Multiply by (1+cos(5x)) in numerator and denominator.

Q: Evaluate the following indefinite integral

A: To calculate the indefinite integral.

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.