Find dt 1- t2 sin (t)

Q: sin 3t dt J cos 3t – 1

A: Given: I=∫sin3tcos3t-1dt   ....(1)   We know that; ∫1ax+bdx=1alnax+b+C And ∫a·fxdx=a·∫fxdx, where…

Q: Find all critical points of the function: R(θ) = cos θ + sin2 θ

A: The derivative is defined as the rate of change of one quantity with respect to another. In order to…

Q: 2. Evaluate the integral / sin'at dt

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Q: sin t cos t dt Jo

A: since u have asked multiple questions in a single request so we will be answering only first…

Q: Prove that  d/dx[cosx]=-sinx

A: We will use the definition of the derivative  Here f(x)=cos(x) So,

Q: Compute d/dx  sin-1 (x/x+1)

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Q: a.) [ sec²(t − 1) dt b.) 2 √t c.) [ sin(Int)

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Q: Q2 : Evaluate the integral sin x dx 1-sin² x

A: To find the integrations.

Q: Find the definite integral.

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Q: t sin(2t)dt.

A: Given : ∫tsin2tdt

Q: sin t dy If y = tan" ), show that cos t-1 dt 2 II

A: Formula Sin2x + cos2x =1  Find dy/dt

Q: d Prove that 1 da (sin-1æ) = V1 – a? -

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Q: | t sin(2t) dt 1.

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Q: 1. Differentiate the function. y = In(VT sin-(5æ))

A: As per our guide lines we can answer only 1 question. Kindly post the other question seperately.…

Q: ÿ + ỷ = sec t tan t

A: This is the question of the differential equation.

Q: (b) Show that 1 2t and sin x = cos x= 1 +? 1 + ? (c) Show that dt 1 + f dx %3D 2.

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Q: Find 19. t sin 3t dt Jo

A: Topic:- integration  Note:- as per our guideline if more than one question uploaded than only first…

Q: 1. If f(x) = sinx, show that f(x + y)-f(x) = cos x siny - 2 sin x sin² 2 2Y-T

A: 1) Given f(x)=sin(x)

Q: tan x If h(x) Vt + vt dt, then find ht(x). 0,

A: We apply here Leibniz rule

Q: Find cosh² (t) sinh5 (t) dt.

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Q: 2. Differentiate. f(t) = et sin(2t)

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Q: 1- f(t) = 2t³; 3–f(t)=sinh(2t); 5-cosh (t) sin(2t);

A: Given :1. f(t)=2t33. f(t)=sinh(2t)5. cosh(t).sin(2t)

Q: / sin(In |x|) cos(In |æ|) + dx COS -

A: We have to prove that the given integral is true.

Q: Find the length of the curve f(x) = ln(sin x), 0 ≤x ≤π/6.

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Q: 8. y = In(2e-t sin t)

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Q: -6e' sin(at – 3) dt

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Q: Find the most general antiderivative of the function. f(x) = 5 cosx-7 sinx

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Q: Q) - Find of y = sin de dy ! -11

A: Siny = 1/x.

Q: Q! O show th at [x sin'x + V1-x²] = sin'x sin x

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Q: 10. J(3x3 — 5х + sin3x) dx -

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Q: 2. Find the length of the curve: y = 2 In (sin (÷x)); -< x

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Q: Show that sin x dx=1-cos t (0<x<t<}r).

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Q: dx1 2.x1 + x2 + x3 + sin(t) dt dx2 = -x2 – 2x3 – 2 cos(t) dt dx3 2.x2 + 3x3 dt

A: According to the given information, it is required to find the general solution.

Q: tan st e dt 2

A: “Since you have asked multiple question, we will solve the first question for you. If you  want any…

Q: find ds/dt. s = tan t - e-t

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Q: find dy/dx. ƒ(x) = x3 sin x cos x

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Q: : (a) Evaluate S cosx sinx V1 – sin+x_dx. (b) Evaluate S V1 – x² dx.

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Q: ds Find dt 1+ tan t S= 1- tant

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Q: Find fif f'(0) = 2 sin 0-sec²0

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Q: 13. F(x) = sin t dt 20

A: We need to definite integral properties  also integral of sinx is -cosx

Q: T sin x – cos x dx

A: Given data: The given integral is I=∫0πsinx-cosxdx. The given integral can be written as,…

Q: Find dy if sin x + 1 = cos y dx²

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Q: e) Differentiate f (t) = (e-6t+ sin(2-t)) -9- %3D

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Q: Show that ∫∞−∞ sin x dx diverges.

A: To Show: ∫-∞∞sinxdx diverges.

Q: cos x -dx Compute the integral 1+(sin x)²

A: replace sinx=u cosxdx=du limits of u will be 0 to 1

Q: dx b) sin 2x sin x dx (3x + 2)²

A: we have to integrate

Q: Compute f sin(cos(x²)) sin(x²)x dx

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Q: tan-1 (xy)=3x2+sin-1(y) find dy/dt

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