Q-1: Integrate each of the following without using trigonometric substitutions (a) S: cos(x) xp- sin(x) +3 dx (b) J | T/2 (c) V1 - sin?(x) dx

Q: (8 cos x + 9 sin x) dx

A: SOLUTION-

Q: cos 5x dx 2. S 3 + sin 5x

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Q: cos 2x he ƒ -dx is 4+sin 2x {A} In|4 + sin 2x| + C {B} In|4 + sin 2x| + C {C}(4+sin 2x)² + C {D} -(4…

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Q: (b) ſ sin³(x) -dr cos (1)

A: Let's solve given integration.

Q: S sin5 3 x cos' 3 xdx

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Q: 5 cos2(x) sin(2x) dx

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Q: 2. (sin 0-2r cos 0)dr + r cos 0(2r sin 0 + 1)d0 = 0

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Q: i) Find sin 6x+ cos 4x dx. 3 ii) Evaluate || et -dx . Hence, solve 2e* dx . (* +2)" +2

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Q: sin(4x) cos(2.x) dx n (2x) sin (6x) cos (2x) cos 2. ()= 4 'cos (2x) cos (10x sin (2x) trts 10 (e)…

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Q: f cos(x³) x² dx. O 1 ¹ cos4 + c 4 1 3 sin x²+ C 1 1 ¹ cos4 + c - 4 -3 si sin x³+ C

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Q: 57 sin 6 (똥 + 미) =글(c8 )%3D (cos w - V3 sin w) -

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Q: 1. f/² sin () cos (+) sin (²) d dx (Consider initially the first 2 terms)

A: We have to use the formulas for 2sin(A)cos(B)-sin(A+B)+sin(A-B) and 2sin(A)sin(B)=cos(A-B)-cos(A+B).…

Q: cos

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Q: /2 2 cos x dx 1+ (sin x)² -n/2

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Q: 6. Evaluate A sin³ x cos4 x dx.

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Q: π/2 COS X 1 + sin² x dx

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Q: 5. (sin 0 – 2r cos² 0) dr + r cos 0 (2r sin 0 + 1) d0 = 0

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Q: cos(2x) dx 1 In |1 – sin(2x)|+c 2 - 1 – sin(2x)

A: Note: It is assumed that the question is asking to test of the validity of the given equation.   It…

Q: 18. sin³ x cos x dx

A: Here we will use substitution method for solving this problem

Q: 3. KIN 2 13² cos x V1+sin x dx

A: The given integral, ∫0π2cos x1+sinxdx

Q: (2) S sin6 x+cos6 x sin³ x cos³ x dx

A: See this solution in below.

Q: 1. ² sin() cos() sin(x) dx (Consider initially the first 2 terms)

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Q: S cosx. sin“x. dx = cos³x + C sinx + C O None O sin*x 4 + C

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Q: 1. S 2x sin-1 x² dx. 2. S sin² 20 cos³ 20 d0. 3. S sec? x dx V1-tan?x

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: 3. S sin³ 0 cos³ 0 d0

A: Given

Q: 4x /² sin () cos (+) sin (²) dx (Consider initially the first 2 terms) 3

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Q: cos x 3. f sin³x dx (2 + sin?x) + C 3 4. S* x sin 2x dx 1-9x2 5. S sin-1 3x dx + x sin-1 3x + C 3

A: Q - 3

Q: cos(x) + s(3x)+ 25 cos(5x)+..) 4 Ans. + sin(x)- sin(2x)+ sin(3x)– ...

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Q: 6. f(t)=-e" sin (2r + 7) -2t 7. f(1)= 3e " cosh (In 21) %3D

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Q: 4 + cos t -dt 1 – sin t

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Q: 3. fe2x+Inx² sin x² dx = = 2x -+√e²x cos x² dx

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Q: 1- cos(0) (d) de sin (0)

A: We have to find integration

Q: O 1:0: d (sin-x?) = (sin-1; dx 1 d V1 - x² dr (x²) خيار 4 1 V1- x4 2x V1-x2

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Q: 1 COS 4 Now, differentiate f'(x) with respect to x. - 4 -x* sin(x4) f"(x) = -x°•si Submit Skip (you…

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Q: 1. f cos³ 3x sin¹ 3x dx 2. fcsc4 5x cot4 5x dx 3. ƒ cos³ xdx from a = 0 to b = 2

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Q: 39. cos (T + x) 40. sin (2m- xr) 學一) 37T 42. cos 41. sin -

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Q: B sin 5x+ sin 3x 1 sin 5x+-sin 3x+c 6 I 10 fcos 4x cos.x dx = ?

A: Given :∫cosxcos4xdx

Q: •π 2 (sin³r)√1 (sin³ x)√1 + cos x dx

A: Given problem:-

Q: 2 0 sin 2x dx 3-cos2x

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Q: 4. S(1 – cos 4u) du 5. S sin x cos x dx

A: 4) Given:        ∫1-cos4udu Apply linearity:    =∫1 du-∫cos4u du     =u-∫cos4u du

Q: k. [₂ x cos³ 2x sin 2x dx

A: According to the company rule we can answer only first question and rest can be reposted.

Q: Q-1: Integrate the fraction of functions: 1. f- 14a+1 2. sinx- V(1-x) 2-7x-4x2 dx 3. SE 1-sine dep.…

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Q: n/10 n/4 (1 + sin x)dx cos? x 1. 2. V1 + cos 5x dx (х - 3)dx x2-6x + 10 dx 2 4. 3.

A: Acc. to Bartleby guidelines, I am solving only 3 parts .  If you want more to be solved ,then upload…

Q: 6. Using a suitable substitution in each case, integrate the following w 1 (a) x2 + 10x + 29 sec?,…

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Q: 3. y³x2 – cos- sin x² + esin x = 1 y DIFFERENTIATE THE GIVEN

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Q: 3 5. cos x dx > 6. sin x cos x dx =

A: According to the trigonometric ratio:  sin2x + cos2x = 1 Integration of cos x is sin x.

Q: 4x 3x + cos (2x² + 1) tan? x) x (1+ sin² dx

A: Here We have to evaluate;  a) ∫4x3x+cos(2x2+1)dx b) ∫tan2x(1+sin2x)cos2xdx

Q: */2 2 cosx dx 1+ (sin x)2 -n/2

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