0 5. χ √√ x³ sin dx = S: x3 3x² sin x X2 -2 cos 6x -4 sin X 8 cos x 16 sin NIX

Q: ff2yx² + 2 sin(2x) + coś (ny)dA if R = [-2, 1] × [0, 1] X

A:

Q: Rewrite – 2 sin(r) + 3 cos(x) as A sin(z + o) A = $ =

A:

Q: 47' sin z = x³ . cos z + sin z - 3z² Select one: True False

A: Given that d(x3 sinx)/dx  . Here we derivative of this question with respect to x. We know that…

Q: Which of the following is equivalent to | cos(4a)sin (4x) da ? cos udu · 1 sin udu, where u = 4x…

A: The answer is found in step-2.

Q: 2 cos @ dӨ . 1- sin 0

A:

Q: 1-COSC 1- cosx It cos

A:

Q: x) dx + sin? x + cos? .2

A: Given integral, ∫xx+sin2x+cos2xdx

Q: a. +4 cos x +6 sec x – 5 ) dx 2 x5

A:

Q: | 12 csc² (62) cot(6) dæ = 12 csc (6x) cot(6x) dx : (Use Substitution Method) %3D 12 12 +C 12 sin?…

A:

Q: [6 sin x – 7 sec? x] dx +C - %|

A: Find your answer below

Q: (4) = - V2 -1 cos 4

A: Given,            cos-122=-π4

Q: P8: sin x cos x (2 sin x – 1)(sin x + 1)

A:

Q: Evaluate sin(x) 1+cos(x) -dx

A:

Q: Find !V1-cos xdx 2 sin x = 1- COS X V2(-cos x/2)+ c 1/ /2(-cos x/2)+ c В. 2/2(-cos x/2)+ c С.…

A:

Q: TL (3x −2+ sinx) dx

A: The given integral,         ∫-π4-π23x-1x2+sinxdx

Q: x* + 3 dx x² + 3x + 1 4. 00

A: Given: ∫-∞+∞x4+3x2+3x+1dx

Q: 1+sin x dx COS x

A:

Q: 46 a Show that cos x+ =-sinx. = -sinx. d" (cosx) = cosx + drn b Prove that

A:

Q: sin(2t). Find Əz Ət if z = √r² + s², r = cos(2t) and s =

A:

Q: 2+ cos (1 + x»'½) .0.5x dx 22 cos (1+x³/2) V1+0.5 sin x 2,0.5x dx|

A: By using Simpson/Trapoizodal rule.

Q: sin x 16. Evaluate f dx cos²x a. tan x sec x + C b. sec x c. sec?x d. tan x

A: Using substitution method Let cosx =t

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

A:

Q: 27. Evaluate: cos 2) - sin 6 4 /3 /2 2 2 1 V2 V3 2 2 1 V2 2 None of the above. + |

A: Hence option (c) is correct.

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

A:

Q: x sin(x? – 1) Vcos(x² – 1) +

A: Given that: ∫-11xsin(x2-1)cos(x2-1)+13dx

Q: 8 0 sin axsin 2 x² bx -dx

A: