sin 0 cos Od0 -u'du FC = - 1 cos“ 0 + C 19.

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A: We'll answer the first question only since the exact one wasn't specified. Please submit a new…

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A: (1) using integration by substitution∫4 cos1x2x3 sin31x2 dxlet   sin1x2=udifferentiate both…

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A: Given: I1=∫sin43xcos33xdx, I2=∫tan4x2sec2x2dx

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A: Given, sec-1x=cos-11x   Check it is True or False:

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A: This question can be solved by applying the formula of cos2x cos2x=cos2x-sin2x

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A: Integration:

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A: Use formula 2sinAcosB=sin(A+B)+sin(A-B)

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Q: 4. y = tan¬1(3x) cos 1 4x 5. y =

A: To determine the derivative of given functions. Here we will use the following formulas-…

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A: Note:- In given problem, according to written way sin2x is multiplied by 3x+1. If you want solution…

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Q: 3 3 | sin sin x cos xdx 5

A: It is integration problem.

Q: cos(4x) cos(2x) sin(4x) sec(2x) 12. Verify: - sin(2x)

A: cos(2x ) =cos2(x)-sin2(x) = 2cos2(x)-1 =1-2sin2(x) sin(2x) = 2sin(x) cos(x)

Q: 5. 4 (secx-1)(sec² x+secx+1) Sª cos² 2x-2 cos 2x+1 -dx

A: Indefinite integral is the process through which one can determine the function which on…

Q: ( sin (In 2x) - cos (in 2x))? +x dx 2x

A: Let's find.

Q: 3 + cos 3x dx Evaluate sin 3x

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Q: 4л coS 씀Cos 즙Cs -sin sin 15 15 15

A: We have to find the exact value cosπ15cos4π15-sinπ15sin4π15.

Q: Find integral.

A: To find the integral  I = ∫sin10x cos x dx

Q: cos x sin x = csc 2x cos 3x sec 2x

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Q: cos(2x)– cosx sin x 4. lim, »o

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Q: sin 2x cos 3х dx

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Q: Si cos°(3x)sin (3x) – cos (3x) sin°(3x) dx

A: First we common out cos7(3x) sin7(3x) and then apply the formula cos2(3x)-sin2(3x)=cos(6x)

Q: sin(2r) cos(2x) +1 2. Prove: csc(2x) + cot(2r). %3D COS

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Q: 1. sin x sin 2x + cos x cos 2x = COS X

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Q: π/2 sin (cos() sin() dx (Consider initially the first 2 terms)

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Q: sin 0- cos 0 = V2

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Q: sin 3x dr + 2y cos* 3x dy = 0 COS

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Q: 9. cos(x-)

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Q: sin 4x cos 3x sin 2x tan 3z dx

A: (NOTE- Since it seems to be a typo mistake so, assuming that in the given integral all the variables…

Q: 1+ cos x sin x 7. Verify: ¹ 11 csc x + cotx

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Q: 3) (sinx + cos x)² = sin 2x + 1 COS %3D

A: We have to prove that  (Sinx+cosx)^2=sin(2x)+1

Q: sin 5x cos 3x dx

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Q: sin(2x) dx cos(2x)+5 2x dx V3x +1 4 sec2(2x) dx ! 3(1-tan 2x)

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Q: 3. x² sin* () dx, x² sin2 () dx, n, n, a is a constant

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Q: cos 2x cos.x+ sin x xp-

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Q: sin 0 cos 0 d0. Jo 0,

A: Here we to solve definite integral.

Q: /² sin ( cos() sin() dx (Consider initially the first 2 terms)

A: To evaluate the value of given integral. Use the identities: 1.sin A cos B=12sin(A+B)+sin (A-B)2.sin…

Q: ) sin(2x) cos(5x) dx Scot (x) csc (x) dx

A: Given: 1.∫sin(2x)cos(5x)dx 2.∫cot3(x)csc4(x)dx

Q: sec(x)cos(3x)=0 from [-pi/2, pi,2]

A: sec x cos 3x=0          [-π/2,π/2] sec x (4 cos3x - 3 cos x) = 0 [cos 3x= 4 cos3x - 3 cos x] 4 sec x…

Q: | sin5 cos cos – dx 3

A: The given integral is ∫sin5x3cosx3dx