Q: 32. y" + y = sec x; y = c1 cos x + c2 sin x + x sin x + (cos x) In(cos x), (-7/2, T/2)
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Q: Evaluate the definite integral.
A: Given : The definite integral is ∫π 3π 2 cos x ( sin x )sin2 x -14 dx .
Q: [1+sin x) 'cos x dx (sin x)4 +C A ) x+ sin x + B -(1+ sin x)*+C (sin x)4 -+C 4 sin x +
A: Substitute, 1 + sin(x) = t
Q: SIn(x + 12)dx = O A. (x+12)In(x+12)23-23x +C B. (x+12) In(x+ 12)- 23x +C OCxIn(x+ 12) -x+ C 23 23 +C…
A: We will use integration by parts to solve this
Q: 7) y=Flx)=cos" (x) A.) xCcoskl) =4 Cos? (x) %ax (coscx) =4 cas? (x) (-sin(x). 4 Cos (x)Sin(x) %3D…
A: Explanation of the answer is as follows
Q: 5. ( sin (7x) cos'(x) dx sin'(x) dx 6. /2 7. cos'0 de 8. Jo sin (20) de
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Q: 1 + cosh(x) 1 + tanh(x) 1- tanh(x) 1 cosh(x) cosh(x) + cosh(x) – He* + e*) + e* - o*) e* + e*) - e*…
A: The objective of the question is prove the given identi
Q: x + sinx dx. Evaluate: 2x- cos/x (A + C 2 2x+ cos/x B + C 2 © x-2cos/x + C x +2cosx+ C E None of the…
A: Let √x=t then solve it.
Q: cos(x ) + æ5.1 dx. )ln(1+x² 3 cos(x Evaluate 1+ el.61x – 68 - 3. answer
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Q: 1 – sin(x) Evaluate: dx I+ sin(x) 1- sin(x) A cos(x) - 2x +C 2[sin (x) – 1] cos(x) -x+C 4cos(x) +C…
A: We have to solve the integration
Q: 5 sin x If f(x) then 2 + cos x 5(1+2 cos (2)) f'(x) = (2+ cos( z))? (2+ cos( x) f'(5) = 0
A:
Q: 3 sin a If f(x) –, then 2+ cos x 3+ 6 cos(x) (2+ cos (z))² f'(x) = f'(5) =
A: For part (b) just put 5 in place of x in the expression of part (a).
Q: S sin(1 – x) (2 – cos(1 – x))* dx A (2-sin(1-x)5 (2-sin(1-x)5 +C +C D (2-cos(1–x)5 +C (2-cos(1–x)5 +…
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Q: 18. y'= (x+ycos x)/(1+ sin x) 2 = (x- 1)(1+ sin x) ( tan x +tan x 3 2 sec® x) +c.
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Q: 6. (F(x) dx where f(x) = sin x if 0 <x < /2 cos x if 7/2 <x<
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Q: Evaluate S sin“ (x) dx 4 Select one: -cos (x) sin(æ) +(x – sin(2a)) + C None of these 글sin'(2)…
A: ∫sin4x dx = ∫(sin2x)2 dx We have cos 2x = 1-2sin2x2sin2x = 1-cos 2xsin2x=1-cos 2x2
Q: lim h→0 (e) cos( 4 + h) h 1
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Q: Sin x 10. y = 2+Cos x 3 2+Cos x Ob. (2+Cos x)? Cos x C. (1+Cos x)2 1+2 Cos x d. (2+Cos x)? Oa.…
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Q: 9. e' cos (x) =1+ sin (xy) 10. tan (x – y) = 1+ x2
A: Given the equations 1)ey cos(x)=1+sin(xy)2) tan(x-y)=y1+x2We need to find implicit differentiation…
Q: | -sinx. cos* x. dx = O cos*x X. + C 4 cos x + C 5 O sin x + C 5 O None
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Q: x sin x cos x Evaluate : dx. sin x + cos'x
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Q: dx 3. Evaluate: S V(x+2)(3-x) A. sin-1 (*) + 3x- C.V6 +x – x² -In |x-+v6 + x – x² |+C B. sin-1 (*)-…
A: As per our guidelines we are supposed to answer only one question.Kindly repost other question as…
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: (1) (sinz) + (cosr)* sin x COS x (2) tan x in terms of sin x, cos x %3D d. d. ( sin x COS X %3D dx…
A:
Q: 1 + sin x Differentiate y = x + cos x
A: As we know that: The Quotient rule: fg'=f'·g+g'·fg2 The Power rule: ddxxn=nxn-1 Given:…
Q: 1. S sin (2x) dx [sin(In x) + cos(In x)]² dr -dx 2. 4 3. S 3x/10 In(3x) – (1In(3x))? xp: 3(cos x)? +…
A: According to bartlybe guidelines I have right to solve only one question at a time..... Please put…
Q: *y=(sin(x)+cos(x))cos(x). dyldx -sin 2(x)+cos*2(x)+2cos(x) -sin 2(x)+cos 2(x)-sin(2x) O
A:
Q: e* sin(e^)ax 8+cos²(e*) (x+2)dx x2-3x+5 .2 dx
A: Given that
Q: 7 (1 + sin² x) = e 2" sin 2.x, y(0) = 1 X 7) dx
A: This equation solve by separation variable
Q: e) S„ =E(-1)". sin (5 +n5) Vn+1 e) S. = n=0
A: Note:- Sum of convergent and divergent series is divergent. cos2x=1-2sin2x⇒sin2x==121-cos2xput…
Q: 1. Integrate x tan- (x²) dx. x4 + 1 2. (a) Evaluate cos? x sint x dx. (b) Calculate dx. x² – 5x + 6…
A: These are integrals which can be evaluated using standard techniques. The solution typed in LaTeX…
Q: et +e» et Рe-* cosh(x) sinh(x) 2
A: Given that:- coshx=ex+e-x2 sinh(x)=ex-e-x2
Q: O 1:0: d (sin-x?) = (sin-1; dx 1 d V1 - x² dr (x²) خيار 4 1 V1- x4 2x V1-x2
A:
Q: (i) (x² + 1) tan-'x – x (ii) x³ loga x + e* cos x d (iii) e2 In cos 2x iv) 102 In cos 2x dx
A:
Q: None c) cosh x + C sinh x +C 2 sinh x +C cosh x +C
A: The given integral, 12∫ex-e-xdx
Q: S sin*x cos³ x dx C sin5x sin'x + C 7. sinx sin'x + 5 sin x cos'x + C 7 D sin5x cos'x + C 7. 5
A: We know that ∫xndx=xn+1n+1Also, d(sin(x))dx=cos(x)
Q: 5. (cos" x- y cos x) dr - (1 + sin x) dy =0
A:
Q: 0sin 2 x coOS x dx
A:
Q: 7. y = x** 8. y = = (x² + 4) In(x² + 4) – x² 9. sin y = ln(x + y)
A:
Q: P8: sin x cos x -dx J (2 sin x – 1)(sin x + 1)
A: ∫1au+bdu =1a lnau+b+C
Q: 4 sin x cos x + 2 sin x - 2 cos x - 1 = 0
A: first factorize the given equation and than split two product equation detailed solution is given…
Q: 5 sin x If f(x) then 2 + cos z 5(1+2 cos( z)) - cos (x))? f'(x) = f'(5) =| 0
A: Please refer the attached image for complete solution. THANKYOU.
Q: 3 Evaluate S ( - 4 sin x + Vx) dx
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Q: 1. Using Half Angle Substitution cos x dx Find= S 2-cos x
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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: dy sin x Find in y = dx 1+ cos x 2 2 2 cosʻ x+ sin´ x+cos x cosʻ x+ sin´x а. b. (1+ cos x) (1+ cos…
A: Topic :- derivatives
Q: f(x) = e-x (3.2 sin(x) - 0.5 cos(x))
A: Here a simple python script written follow that.
Q: e Lim 2. 5+s2 y4 3 Lim (4) Lipn J+ Cos늦
A: 1. lims→∞(ss+1)(s25+s2)lims→∞s×s2s×s211+1s11+5s2= 12×2=14
Q: Find the general solution of y''+ y =1/cos x
A:
Q: |2tan x In (cos x) dx= A sin x [In(cos x)] + C (B cos x [In(cos x)] + C В C [In(sinx)]? + C D…
A:
Find Dy/Dx
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