cos x 4. Compute the integral 1+(sin x)? Hint: u-substitution

Q: Evaluate the integral. |sin° (x)cos“ (x)dx

A: In this question, the exponent of cos(x) is even i.e. 4, and the exponent of sin(x) is odd i.e 5,…

Q: How to compute Cp using below equation, OP, sin 0; Cp, = 2 sin? 0; +2 cos 0 dy dy Where y = 0.5x…

A: To simplify: CPi=2sin2θi+2dθdyisinθi∫0yicosθdy

Q: cos(x)In(1 + x²) + æ4.8 dx. Evaluate 1+ el.69z – 42.8 answer =

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Q: S x dx x²+√√x²-1-1 The integral substitution? (A) [sec²0d0 1+tan cose de (B) 1-sine sece tane de…

A: Simplify and substitute x = sec θ to get the answer.

Q: Evaluate (sin z + cos x) da using by term by term integration 0. Answer:

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Q: Homogeneous Find C, if y f(cos 2n) = tan 45° 3(3x + y?)dx-2xydy 0

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Q: Find the antiderivative using the indicated substitution. (Use C for the constant of integration.)…

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Q: Recall that cos™ 1 x = arccos x. Find r1/2 a sin(cos a) d. 1

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

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Q: The integral S³ S S Sse x dx x²+√√x²-1-1 sece tane de sece - 1 cose d 1 - sino sine de 1 + cose…

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

A: Evaluating integral by trignometric substitution

Q: 2. Evaluate the Trigonometric integral. C (a). S sin(2x) cosxdx. rT/2 (b). S cot?xcsc*xdx. T/4

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Q: Find the indefinite integral. |x cos 9nx? dx х сos Step 1 To find the indefinite integral x…

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Q: 12 Which expression represents the trapezoidal approximation T3 to the integral sin (V7) dx?

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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: Q1/: Evaluate the Trigonometric integral m/4 V(1+ tan?x)3 dx -a/4

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Q: dy - y = x? sin(x) dx

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Q: Given y cosh' (x-3). Based on the given function show that d'y d'y 4 sinh (2x) dx dr dy -[tanh(x-3)]…

A: "Since there is a typo in the problem, I made a correction to get the result and proved it".…

Q: /4 sec? Vwdw a) b) sin 2.xcos xdx c) f tanh xdx

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Q: 3 T lavi cos x + sin x %3D

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

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Q: Given: S√-x² + 4x+5 dx. Using trigonometric substitution, what is the integral form in terms of ? 9…

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Q: dy 1-5e + y cot x 5e", with y(z/2) =-4. Cos 7) %3D Ans.: y = dx sin x

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Q: integral od pi/4 0 sin^5 θ dθ

A: A detailed solution is given below

Q: Evaluate the integral by following the steps given.

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Q: Q1: To integratef 6x + 8 dx we substitute a)x = sec 0 + 3 b) x = tan 0 + 3 c)x sec 0-3 d) x 3sec 0…

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Q: 0,00 Puanlar) What is the value of the integral / sin(6x) arctan(sin 3x)dx? n- 2 a) 3(n - 2) b) c)…

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Q: Z=sin(X) + cos(Y) X from 1 to 10 (increments of 0.5)

A: % Matlab script to create 2 subplots (mesh and surf) % create the matrices X, Y both between…

Q: The integrating factor that can be used to turn the following non-exact equation into an exact…

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Q: 3x 5cos(x)sin (r) dæ. Evaluate the definite integral

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Q: The coefficient of sin(x) in the antiderivative of F(x) =| cos 2 %3D

A: Given: F(x)=cosx26

Q: (z*sin - 2° cos 2y cos r2 y? dr+2xy cos ,dy = 0.

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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: Jsing substitution with u = sin(2x), the definite integral sin3 (2x) cos(2x) dx is equivalent to u³…

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Q: dy There is no need to simplify. dx 2. Find cos- (sin x) – sech(tan-x) a. y = ecosh a

A: Find your answer below

Q: '/2 Q4/ Find the Definite Integral cot 0 csc 0 de

A: Given: I=∫π4π2cotθcsc2θdθ...1 Use the substitution method to calculate the integral value.…

Q: Directions: evaluate the following integrals sinx 4. S –- dx cosx./cos?x-25 3 5. S. dx secx -

A: To evaluate the following integrals

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

A: Use substitution

Q: Using substitution with u = sin(2z), the definite integral si "sin®(2x) cos(2r) dr is equivalent:…

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Q: Check for exactness and obtain the general solution. 1. (2xy – tany)dx + (x2 – xsec?y)dy = 0

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Q: at (x = })? dy Csc(3x) Sin(3x) + Cos(x), Find Let y =

A: The given function is: y=csc(3x)sin(3x)+cos(x)  =csc2(3x)+cos(x) To find the derivative of it:…

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

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Q: (b) Evaluate the given trigonometric integral sin r dx (x² + 1)(x² + 9)

A: The given integral is ∫-∞∞sinx(x2+1)(x2+9)dx. It is of the form ∫-∞∞f(x)g(x)sin(nx)dx. To solve this…

Q: 11 sin y Evaluate the integral e" cos y dx dy. NOTE: Enter the exact answer. 11 sin y e" cos y dx dy

A: The objective is to evaluage the integral.

Q: sin z VI+ cos I

A: To evaluate: ∫sin x1+cos xdx

Q: ind general solution by separating the v y3 = (y* + 1) cos x %3D dx.

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: d²y dy + 2y sin? x = e-cos * sin² x dx Solve : + (3 sin x – cot x) dx?

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Q: Solve A = sin(t²) + t, x(0) = 20. It is OK to leave your answer as a definite integral. %3D %3D

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Q: What is the value of the integral f sin(6z) arctan(sin 3r)dr? a) 3(7 – 2) b) c) d) 6(* - 2) e) - 3

A: Let  I=∫0π6sin(6x)·tan-1sin3x dx =∫0π6(2sin3x·cos3x)tan-1sin3x dx   ∵sin2x=2sinx cosx Assume,…