With the substitution u = sin(x), we get | 11 sin2(x) cos(x) dx = 11 u2 du. u? du. 11 %3D which integrates to

Q: Find dy/dx in terms of z and y if cos² (3y) + sin² (3y) = y + 15. I

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Q: 3 4) Find / sin (2x) cos (2x)dx

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Q: QI) Show that: (a) (1+x)° =1+6x (b) (cosx) = –sinx dx

A: 1.  a  1+x6≅1+6xb  ddxcos x=-sin x

Q: te √e³x Evaluate 3x cos 4x dx.

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Q: Solve dy dx cos x = cos x cst ² y

A: A differential equation can be solved using the variable separation method. In this method, the…

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

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Q: cos 2x 12) S 2cos2x sin x – sin x dx -

A: To integrate:∫cos2x2cos2xsinx-sinxdx Solution: ∫cos2x2cos2xsinx-sinxdx On simplifying further we…

Q: dx (x²+4x+13)3/2 ſcos5(x)sinª(x)dx f) S g)

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Q: Integrate (sin1/2)(x)dx

A: The given integral is ,∫sin12x dx=∫sinx2  dx

Q: 7. In the absence of predators, the population of mosquitoes in a certain area increase at a rate…

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Q: y = 2 sin 3x 1+3 cos2x

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Q: (- + 2 cos 2x ) dx + (- - 2 sin 2y ) dy = x2

A: You have asked multiple questions in a single request. As per our honor code, we will only solve the…

Q: 1 7. sin0 tan0 + cos0 = %3D cos0

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Q: If y = cos 3X find dy/dx: y = cos?3x = (cos 3x?. (cos 3x )?. %3D

A: Given, y=cos23x=cos3x2

Q: d (x2+2x)(sin(x)+5) 7. Find: dx Зx+2

A: To find:

Q: 4 sin (2x) dx cos (2x)t4

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Q: Evaluate cos(x) - 1| dr.

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Q: If f(x) = sin?x, then f"(x) = %3D A 2cos2x B cos2x -sin2x D -4sin2x

A: Given, f(x) = sin2x For the given function , applying chain rule ,  First differentiate it as { xn ,…

Q: 8. d.x 1. 3 cos 2x + 1

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Q: Find d²y/dx² if y = =x cos(3x) — sin²(x). -

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Q: 1° cos(3r) dr COS

A: Given, ∫x2cos3xdx  We have to evaluate the integral.

Q: y = cos((TX)5)

A: Please see the white board.

Q: у%3D sin(4x — 2) cos (4x + 2) || -

A: topic - derivative