Show that 5000 roo sin(rw) sin(rw) 1-w² dw sin(x), 0≤x≤ π, 0, X > T

Q: Show that J (x) = 2 sin x

A: By definition,                  . Now,  we need to prove the above statement by taking n = 1/2.

Q: Find dt 1- t2 sin (t)

A: Solve the integration

Q: D?/if w= Cos (X+y)+Sin (X-y) Show that

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Q: t' sin(2t n(21*)dt Evaluate

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Q: Show that for x > 0, sin ¹x+cos -1 X = FIN 2

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Q: Find y" of sin y + cos x = 1 using implicit differtiation

A: Given Data: Equation: siny+cosx=1 ......1   The first differentiation of equation (1) using the…

Q: Evaluate sin dx

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Q: d 1+ sin² (2)| dz

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Q: QS A) Find IF y = - Ve IF y =-Vt and t sinx

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Q: 2t Show that f/² sin tdt ≥ 7. (Hint: sin t ≥ ㅠ over [0, 1].)

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Q: Find f. f"(x)  =6 x + Sin x

A: Given: f"x=6x+sinx we know that f'x=∫f"xdx                                      ..1 so, by using…

Q: Integrate f(cos x)e*+sin xdx B. e-sinx +C A. -et+sinx + C c. ettsinx + C D. e+sinx C

A: Note:∘ddx(sinx) = cosx ∘ddx(a) = 0                                         where a is constant∘∫etdt…

Q: Is the function h(x) = 3 cos x+ sin x concave up or down at the point 3 я?

A: Given:

Q: 10. f sin³x dx

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Q: c) Sa* sin*x dx

A: To evaluate : The integral  ∫π43π4 sin4 x dx .

Q: 7. f sinx cos³ xdx

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Q: EX/ Find dy for function y = sin ³x + cos³x dx H.W Aus=3sinex (Sinx-Cox) 2

A: Note:-Since you asked multiple questions, according to our policy we can answer only first question…

Q: Show that Sx cos*x dx = (x² + x sin 2x +cos 2x) + c

A: Given: ∫xcos2x dx=14x2+xsin2x+12cos2x+C.

Q: Prove that fx" cos(2x)dx=sin(2x)-[x n sin(2x)-x-¹ sin(2x)dx. Do not use Table Entries. H

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