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

Q: Find the derivative of O2 sec 2x O 2tan 2x O-2 cot2x O 1/cos2x y=In sin 2x

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Q: Evaluate the integral. |cos 7x cos 3x dx

A: The given integral ∫cos7xcos3xdx.

Q: Find integral.

A: Given: Let I=∫2x cos x2 dx To Find: To evaluate the given integration.

Q: Evaluate the integral: 2 sin(3x)cos(3x)dx A B 1 4/6 —— 1 wlr 3 1 - wlw

A: Given ∫π3π2sin(3x)cos(3x)dx

Q: Find y, of (D² + 1)y = sec x = In |cos x| (cos x) - x sin x В y = x sin x + (cos x) In sec x = x sin…

A: Please see the below picture for detailed solution.

Q: find /x – x² - dx xV4x – x² dx 9. 10. х dx dx 11. 12. xV7 – x² xV7 + x² Vx² (4 x² 4 dx 13. 14. х sin…

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Q: Differentiate : a. y= 9x sec (x/3) b. y= sin2x/1-cos2x

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Q: Q3. Show that дхду for дудх f = x² siny – 2y³ cos2x (

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Q: Calculate for w-z sin(xy+).

A: The given function is w=zsinxy4+9z

Q: If y = √√1-x² sin¹¹x, prove that (1-x²)+xy=1-x². dx

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Q: Show that : y' = 1 when y(x) = sin-(x) %3D V1– x2

A: Differentiation is done in many ways. Some of the rules of differentiation are illustrated below :…

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: x'+y° Q4. If u = sin- sin-'( -), Show that x+y ди X- ди + y- = 2tanx (2 + ду

A: If u=sin-1x3+y3x+y, then show that x∂u∂x+y∂u∂y=2tanx.

Q: 1od of undc cients, obtain the general y" – 2y' – 3y = 2 sinx

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Q: (1-1/2 x^2)cos x 3. y = 2cosxsin2x-sinxcos2x 4. y= x^3 - x^2cosx + 2xsinx + 2

A: Differentiation: 1.y=sinx2+cosxdydx=(2+cos x).cosx-sinx(-sinx)(2+cos…

Q: Evaluate the integral. sin (3t + 17) dt cos (3t + 17) sin (3t + 17) dt = - 2, cos (3t + 17)

A: Consider the integral

Q: Ssin x x cos x dx = %3D Select one: а. -cos 2x +C 4 b. -cos x + C 4 c. -sin 2x + C 4 d. -sin x + C 4

A: We need to evaluate the following integral ∫sinxcosxdx

Q: Show that bothy= sinx and y = cos x satisfy y" = -y

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

Q: The derivative of y = 3cos(8x+6) is: 1. y' = 24 sin (8x+6) 2. y' = -24 sin (8x+6) 3. y' = -24 cos…

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Q: 1) Find the derivative of f(x) = 1+sin 2x %3D 2 cos3 x

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Q: S2ta J 2tan x In (cos x) dx=

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Q: [2 2 sinx cosx + 3cosx7 2 cosh 3 X 1 D²+ 4 D3 D³ -27

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Q: roo sin(2) Compute (4) dx. fo x(x²+4)

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

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Q: This is exercise 12 of Section 7.5 page 460. Find the integral sin(2x) dx +C 1+ sin (x)

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Q: 9. tan 4x sec24xdx d. cos 5xsin 5xdx e. x sin(3x² +1)dx f. [x* cos(2x' +1)dx

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Q: cos (6x) cos (3x)dx

A: Solution :∫cos6xcos3xdxNote…

Q: f(x) = cos (In (3x))

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Q: (2x) Sinx 2. Prove that (1) Jy₂ (x)=√√(x) =_ (11) J-y₂(x) = √(3/1²) Cosx

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Q: compute (x2 - 8x +20) dx on the interval (0,1)

A: To evaluate the given definite integral over the open interval (0,1)

Q: The answer of integ ra Ssinzx cos3% dX

A: We have to evaluate the given integral.

Q: Q3 : prove that : cosh?x + sinh²x =coch2x

A: L.H.S.:=cos h2x +sin h2x=(cos hx)2 +(sin hx)2  =ex+e-x22+ex-e-x22=14(ex+e-x)2+(ex-e-x)2

Q: 13. To evaluate f 2costx-1 dx, the integrand can be transformed to 1-sin²x a. [(3cos³x+csc²x)dx b.…

A: Here we have to transformed the given integrand.

Q: Find if dy dx y = (cos x) * O (cos x) * (-sin x) O (sin x) * (In cos x - x tan x) O (sin x)* (In cos…

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Q: The second derivative y" of y = x3 + ex – sin(2x) is . 1. O y" = 6x + eX – 8 sin(2x) 2. O y" = 3x +…

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Q: Find S(3/(x) + cos7x + 4 + 20) dx None x1.5 sin7x + 4log x + 20

A: Now,  We will find the integration to the given problems.    Integration of cosec2x dx = - cot x +c

Q: Evaluate the integral. S sin (7x - 10) dx ㅇ cos (7x-10) +C -cos (7x - 10) + C cos (7x - 10) + C 7…

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Q: Find the derivative dy/dx of y = cos 3x O 3 sinx О З cosx O 3 sin 3x О З сos 3x none of the above

A: We can do this by doing derivative both side.

Q: Find the linearization of ƒ(x) = sqrt(1 + x) + sin x - 0.5 at x = 0

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Q: Find the derivative. 3t cos (t) dt %3D O 3x cos (x4) O &va cos (x4) O 3 cos (x4) - 3x sin (x4) O cos…

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Q: Evaluate the integral. dx JSlx2 - 3 sin 1 33 x + C 3 sec1 |9x - 3| + C sec 1 19 x| +C * sec 13/5 x|…

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Q: +15 - If y = cos-1(x) , Prove that dy -1 %3D dx /1-x²

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Q: Integrate by parts f(x)=sin4(x)cos3 (x) dx

A: Given the integral  I = ∫cos3(x) sin4(x) dx cos2(x)=1−sin2(x) I = =∫cos(x)(−sin4(x)(sin2(x)−1)) dx…

Q: Verify the differentiation formula.

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Q: If f(x) = A B tanx 1+e 1+1² 1+e¹ In (secx) √ 1+tan²x 1+ e tanx sec 3x tanx -dt, then f'(x) equals

A: solution:-f(x)=∫0tanx1+t21+etdtApplying leibniz integral…

Q: find tan x dx x² x² tan¬' x dx 19. 20. sin 3x cos 2x dx 22. sin 2x cos 3x dx S sin sin 8 sin 4t sin…

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Q: Differentiate with respect to the independent variable. f(x)= (e^x + cos x)^6 (3x^4 - sin x)^2

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Q: on the right. Prompts Submitted Answers D Ssin(3x)sin(4x)dx S(cos(x) - cos(7x)dx} Jsin(3x)cos(4x)dx…

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Q: Compute f sin(cos(x²)) sin(x²)x dx

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