Use the double-angle formula cos 2x = 2 cos x – 1 to evaluate the integral 1 1+ cos 2x dx

Q: dx 3 cos x+2 sin x-5

A: This integral can be solved by using the trigonometric formulas of sinx and cosx in terms of…

Q: Given the integral [sec (x - 1) tan4 (x − 1)dx, which of the following equations will be useful for…

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Q: Watch the video on the integral of sin(ax)cos(bx) and the video on the p two cosines with different…

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Q: Evaluate the integral: 2 sin(3x)cos(3x)dx A B 1 4/6 —— 1 wlr 3 1 - wlw

A: Given ∫π3π2sin(3x)cos(3x)dx

Q: Find cos (z+2) dx. O-sin (x + 2) +C O sin (x4 + 2) +C O sin (x* + 2) +C sin (2* +2) +C

A: Let's find.

Q: By making an appropriate u-substitution, one has that sin(3x² – 2) dx = 1 a · sin(u) · du u + 2

A: Given: ∫sin(3x2-2) dx=∫a.sin (u).1u+2bdu

Q: Evaluate the integral. 1/2 | [2 cos ti- 3 sin 7t j+ sin? 2t k] dt

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Q: Evaluate sin (3x) cos (6x) dx Select one: cos(9r) A cos(3r) tC 18

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Q: S sin° (3t) cos(3t)dt Evaluate COS

A: To determine the value of the integral.

Q: The value of integral (cos(4x)+cos(81)) dx

A: We have to determine the integral

Q: To evaluate 3cosx -1 1- sin?x dx, the integrand can be transformed to A J(3 cos x - sec²x) dx ® S(3…

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Q: Evaluate the integral 1—е-4а sin x cos 3xdx

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Q: Evaluate the integral. 7/2 cos 6x dx COS -T/2

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Q: Find the first and second derivatives of r = [3 cos 2t, 3 sin 2t , 4t].

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Q: Find , where : = sin (a²) cos (y*) O 2.r sin (a²) cos (y²) O 2r sin (x²) 6.x sin (a²) cos (y²) 2x…

A: We have to find partial derivative of z  with respect to x.Given a function of two variables, ƒ ( x,…

Q: sin 20 d0 J Vcos² 0 + 16 V cos?

A: Integration is summation of discrete data. The integral is calculated for the functions to find…

Q: Evaluate the integral. sin 8x cos 9x dx

A: Given that ∫sin8xcos9xdxSolution :…

Q: Evaluate the integral. ∫ Cos2 x Sin2x dx

A: Given :           ∫cos2x sin2x dx

Q: The value of the integral (x–1)* sin (x 1) (x-1) +cos (x-1) is

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Q: use a geoetry formula to find the exact value of the definite interval (-2x+4) dx on the interval…

A: The given function is (–2x+4) with the interval [0,3].

Q: Find the first approximation to the root of the equation xe" – cosx =0 using Regular-Falsi method…

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Q: Prove that: cos(nx) - cos(na) cos(x) – cos(a) sin(na) sin(a) dx = n neN, a ER - {0}

A: To solve this question take different values of n and calculate LHS and RHS separately.     if…

Q: Evaluate the integral sin x dx (2 + 3 cos x)2

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Q: Evaluate the integral ∫cos√θ/ √θ sin2 √θ dθ

A: We have to evaluate the integral: ∫cosθθ sin 2θdθ We know the trigonometric identity, sin 2A=2sin A…

Q: evaluate the definite integral.

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Q: The integral O cose de 1-sine sec²0 de 1+ tan sece tane de sece - 1 S sine de 1+ cose x dx can be…

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Q: state what method applies and how one applies it, but do not evaluate the integral:

A: Given integral is We will evaluate the integral by substitution method.

Q: sin x (cos x + 4) dx 1+cos?x

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Q: (a) Evaluate the integral sin* 4x cos3 4x dx

A: a) Evaluate the integral                                 ∫0π8 sin4 4x cos3 4x dx  Let us substitute…

Q: Evaluate: " sin" () cos* () .4 CoS 2, dx .2.

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Q: the integral of tan^2x cos^3xdx

A: we have to find integral of tan^2xcos^3xwe use following rule

Q: Evaluate the integral cos3 x + sin? х+1 dx cos² x (sin² x + 1)

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Q: Given the integral sin(3x + 5) dx cos(3x + 5)

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Q: cos (3x) · (8 sin (3x) – 1) dx = %3D

A: Given that : The integral is ∫ cos ( 3x ) ( 8 sin ( 3x ) - 1) dx  .

Q: Evaluate the integral. 1/2 sin1"(0) cos (0) də

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Q: Evaluate the integral. sin (20x) cos (11x)dx

A: Evaluate:

Q: Evaluate sin z -dx /4 - coS I

A: Use the substitution method and first simplify the integration than integrate.

Q: Use integration by parts to evaluate 16r cos 4r dr.

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Q: Cos 4x b. .J dx,u=1+2 sin4x (1+2 sin 4 x )*

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Q: Use the addition formulas to deriv TT 31. cos(x - sin x 2

A: Prove that cos( x  - π/2 ) = sinx Here we use general formula : cos( A - B ) = cosA×cosB + sinA×…

Q: Find the following integral:

A: Use substitutions to integration

Q: 2T COs x dx

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Q: Evaluate sin integral (4x) cos(5x) dx

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Q: / tan( 4x + 3) dx Evaluate: (A) –In |cos (4x+ 3)|+C 4 B 4 ® -im [sin(4r + 3)| +C В –In |csc…

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Q: Show that n/2 sin x dx sin x + coS X %3D 4

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Q: 2 sin6 x cos⁹ x dx 0

A: See the details solution in below

Q: cos' x dx

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Q: Use a computer algebra system  to find  integral sin 5 x cos 2 x   dx

A: To find the integral

Q: (x² sin(x')dx = 3 %3D

A: Given : Integration of X2sin(X3)dx