Find the most general antiderivative of f(x) = sin x cos x .

Q: Find two antiderivatives of f (x) = cos x. Then determine the general antiderivative.

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Q: Find the antiderivatives of the functions: 1 f(x) = x* – 2x² + sin x a. Зx3+Vx+1 b. h(x) =

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Q: Find the most general antiderivative. dx x2 2x + C V 3x + C O 2V 2x- + C

A: Given integration is : ∫xx+xx2dx  To find the value of the integration.

Q: Find the differential of the function y = f(x). 2x2 + 5 f(x) = X + 5 dy = %3D

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Q: Find the most general antiderivative of the function. f(x) = 3ex + 4 sec2 x

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Q: Find the antiderivative of f(x) = sin^2x

A: Antiderivative=∫sin2xdxsin2x=1−cos2x2So,∫sin2xdx=∫1−cos2x2dx=12∫1−cos2xdx=12∫1dx−∫cos2xdx=12x−∫cos2x…

Q: Compute for the general antiderivatives of the functions 1. [2 sin x cos x dx 2. ſe2x dx

A: Given integrals, 1. ∫2sinx cosx dx2.∫e2xdx

Q: (a) 2-1 dx

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Q: x In (x?) dx

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Q: find the antiderivative F(x) of f(x)=x^2+sin(x)+3 with F(0=8

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Q: 9. Find the most general antiderivative of the function a) f(x)=12+ sin x b) f(x)= 3x(x-5)

A: see below the answer

Q: sinh x – 1 dx cosh x

A: The given integral: ∫sinh x-1cosh xdxWe need to find the antiderivatives.

Q: sinh x – 1 dx cosh x

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Q: Find the most general antiderivative. dx x2

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Q: y(x* – y²)dx + x(x* + y²)dy = 0

A: Let us consider the differential equation,  Where M and N are the function of  x and y. If the…

Q: Find the most general antiderivative of the function. f(x) = + 3 cos x

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Q: 1. Find the differential of w = x cos y – y sin x.

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Q: Find the most general antiderivative of f(t) = 1 cos(t) – 5 sin(t). Note: Any arbitrary constants…

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Q: What is the integrating factor of y (x² + y) dx + x (x2 - 2y) dy = 0? -1

A: We will find out the required integrating factor.

Q: dx S (x+2)Vx+11

A: Given:  I=∫dx(x+2)x+11 Use the substitution method to evaluate the integration. substitute…

Q: | sec 5x dx

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Q: Figure out these antiderivatives. S dx /1-х2 arctan(x) dx 1+x? ( In(x))* dx 2x

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Q: Find the most general antiderivative of the function. ( Use C for the constant of the…

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Q: Let y = f(x), where f(x) = 3x+6/x+6 Find the differential of the function. dy =?

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Q: 3. x cos x dx

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Q: sin x dx COS x

A: Indefinite Integration Substitution

Q: Find the antiderivative of f(x)=cos(3x)

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Q: i. Je* cos(4x) dx

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Q: of

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Q: Find the most general antiderivative , verify answer by differentiation  g(x)=7sin theta/3

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Q: ■ Find dy /dx  by implicit differentiation ycos x = 1+ sin (xy )

A: The given equation is ycos x=1+sinxy.

Q: 11) Find the antiderivative: f -3+6√x³ √√x dx

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Q: What is the integrating factor of the non- exact DE (4ху+ 3у?-х)dx+x\x+2y)dy %3D0 ?

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Q: For the function f(x) = 2 sec (2x) tan (2x) + sin(x) + cos(x), find the most general antiderivative…

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Q: cos xdx (vii) S 5+sin2 x

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Q: Find the differential dy of the given function. (Use "dx" for dx.) 8 y = 2√x + 4 dx *- (√x +++1)x dy…

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Q: Find the general antiderivative of the given function. sin( x/7π)   and  sec2(5x) + sec2 (x/3)

A: GIVEN DATA : Function sinx7π and sec25x+sec2x3        TO FIND : Anti derivative of the function…

Q: The most general antiderivative of x sin(3x) is

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Q: Determine the most general antiderivative:  f(x) = sec x tan x-2e^x

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Q: approximation of I = [" f(x)dx using composite Simpson's rule with n=4 is:

A: In this question, we evaluate the definite integral by using the composite Simpson's rule for n=4.

Q: E valuate dt + seck tan x dX

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Q: Find the most general antiderivative of f(x) = sinh a + sin x.

A: Given that f(x)= sinhx + sinx. Find antidervative of this function f(x). We know that antidervative…

Q: Find the most general antiderivative. 4 dx

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Q: dx - is 2/x - Sin| x +s|+c. Vx +5 The antiderivativeof - A) True B False

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Q: use the integrating-factor method

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Q: Find the antiderivative of (ex − e−x)/(ex + e−x)9/2

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Q: Find differential of the function y=(x^2+3)^3 dy=? dx When x=4 and dx=0.05, compute the…

A: We have to find

Q: Find the relative extrema of f(x) = (x − 1) cosh x − sinh x.

A: Maxima and minima: f(x)=(x-1)coshx-sinhx f'(x)=(x-1)sinhx+coshx-coshx f'(x)=(x-1)sinhx…

Q: Find the antiderivatives |x In(x²) dx + sec? x dx CO X dx sin5

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Q: What is an antiderivative of x+2 ? x²+1 x + arctan x – 5 2x + 3 x + arccot x x + 2arctan x + 1

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