Steve uses the trignnometric substitution tan ()to evaluate / e) de After simplification, the integral evaluates to i sec (8) – 3 sin (8) +Cusing this substitution Whichof the following is a proper representation of the solution in terms of.x?

Q: Given the integral sec (x - 1) tanª (x - 1)dx, which of the following equations will be useful for…

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Q: Use the substitution t = tan(x/2) to find the integral: 2 1+2 sin a dr Cos I

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Q: Evaluate the following integral. r/4 1 (s secx- cos cos sx)²dx 0 x/4 ļ (secx- cos x)²dx= 5 3 4 8 0…

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Q: Find all solutions in the interval [0,2n). 2 sin 2x sin x-3 cos x = 0 (Type an exact answer, using t…

A: Given :  2 sin ( 2x ) sin ( x ) - 3 cos ( x ) = 0 Interval : [ 0 , 2π )  Find values of x in the…

Q: Evaluate the integral. | 17e3 cos(2x) dx + C NOTE: Enter the exact answer.

A: SOLUTION-

Q: Use the indicated substitution to evaluate the integral. Let x = 4 tan (0). (Give an exact answer.…

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Q: Find Duf at P. 3 4 f (x, y) = sin(3x – 4y); P(4,3); u = i j %3D - - NOTE: Enter the exact answer.…

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Q: Using the trigonometric substitution x = 6 cos 0, 0 < 0 < π, the integral √36-x² x² In cos 0 + C O…

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Q: The integral A B C D S³ x dx x² + √√√x²-1-1 sec²0 de 1+tano sine de 1 + cose sece tane de sece - 1…

A: We have to solve above integral

Q: The coefficient of sin(x) in the antiderivative of Flx)=(cos() is 15/32 (use fraction form not…

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Q: 8 Find the anti denivapine Sfa) faa or © f la) = Cos ( 6x) 16 - Sin? ( 6x)

A: f(x) = cos(6x)16-sin2(6x) ⇒I=∫f(x) = ∫cos(6x)16-sin2(6x)dx Since dsinxdx=cosx, therefore:…

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: Use the substitution formula to evaluate the integral. (1 + cos 3t) 2 sin 5t dt 15 15

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Q: valuate the integral. Jse symbolic notation and fractions where needed. Use C for the arbitrary…

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Q: Prove the left side equal to right side in the following: s2 (eice = (sin at + at cos ar] 1 L-1 (s²…

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Q: Evaluate the integral J (1-cos 3x) dx (Cos 6x=2C03 34-)

A: To evaluate the integral, ∫0π1-cos23xdx

Q: Transform the integral 7 n do d0 by the substitution r = sin o cos 0, y = sin ø sin 0 and then sin 6…

A: The formula for change of variables is given by ∬Rf(x ,y)dxdy=∬Sf[x(u,v),y(u,v)] ∂(x,y)∂(u,v) dudv…

Q: (1 + cos 7t) 2 sin 7t dt

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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: The substitution u = tan |converts the integral 2 π/3 1 dx to: n/2 2 +sin x - coS X

A: Given,∫π22π312+sinx-cosx

Q: Evaluate the integral. | 9e cos(2a) do 3x + C NOTE: Enter the exact answer.

A: As we know that; The expression for the integration by parts: ∫udv=u·v-∫vdu The given integral is:…

Q: Using the substitution t = tan(), the integral 2 dx sin(x) – 78 cos(x) can be written as dt 39 – t-…

A: To make substitution and re write the given Integral.

Q: cos(T/x) x2 cos(T/x) d.x = lim 1 = lim (1- sin(/b)) b-0 T dx = lim sin(7/x) b-00

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Q: The integral O [se Ss S S sec²0 de 1+ tane sece tane de sece - 1 O x dx x²+√√x²-1-1 sine de 1+ cose…

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Q: What is the trigonometric substitution that you would use to evaluate the integral S V5x2 + 10x +…

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Q: Find the length of the curve [x = eª cos(t) y = et sin(t) for 04 (Hint: You can simplify the…

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Q: (1 + cos 9t) 2 sin 9t dt

A: ∫0π1+cos9t2 sin9t dt Consider, ∫1+cos9t2 sin9t dt Put, 1+cos9t=u⇒0-9sin9t=dudt⇒-9sin9t dt=du⇒sin9t…

Q: The integral S (A S- (в x dx x² + √√√x²-1- sino do 1 + cos sec²0 do 1+tano " cose de 1-sino sece…

A: Use trigonometric substitution

Q: The coefficient of sin(2x) t F(x) =(cos() is Blank 1 (use fraction form not decimal no space) in the…

A: To determine the coefficient of sin2x in the antiderivative of Fx=cosx26.

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

A: The given integral is,

Q: The coefficient of Sin(x) in the antiderivative of F(x is 15/32 (use fraction form not decimal no…

A: Given,            The coefficient of sinx in the antiderivative of Fx=cosx26 is 1532.To find : Show…

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

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Q: Given the integral secº (x - 1) tan* (x − 1)dx, which of the following equations will be useful for…

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

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Q: In the next integral S substitution is considered 2x = 5sin 0, after performing the trigonometric…

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Q: Use the indicated substitution to evaluate the integral. 13/2 x² dx, x = 13 sin(0) %3D V169 – x2…

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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: Evaluate the integral. 1/2 |[ cos ti- 3 sin 5t j+ sin? 6t k] dt 1/2 |[cos ti-3 sin 5t j + sin? 6t k]…

A: we use Trigonometry identities to solve this integration

Q: The resulting integral of sin-cos-sino de 2 2 has the form -(0)+ C· What should be the value of o to…

A: I am going to solve the given problem by using some simple calculus to get the required result of…

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

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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: Use the indicated substitution to evaluate the integral. • 7/2 dx, x = 7 sin(0) V49 x2 (Give an…

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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: 2. For ba constant, use results of the recursion relation andSr,(7)dr to derive formulas in terms of…

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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: Make the u-substitution 2 sin x = 2u 1+u²' COS X 1- u² 1+ u² and dx = du 1+u² to convert the…

A: Using substitution evaluate integral

Q: b2 - a? use this result and the fact that cos(x) dx = 1, together with the properties of definite…

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Q: Calculate the improper integral cos(a) dæ x2 + 16 R =

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