1. sin (3z) cos5(3z)dz

Q: 5- S(cos3x – 2) sin3x dx

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Q: b) S sin 2 x cos x dx

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

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Q: for 2 sin (xy t 22) W ニ

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Q: y + (cos x) y =3 sinx.cosx

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Q: Find if, y - x = sin(xy)

A: In this question we will use differentiation property for solving this question and after that we…

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

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

Q: (b) S tan3 x sec² x dx c) S sin³x cos5 x dx

A: The explanation of the solution is :

Q: S(sinx – cosx)²dx COoSx

A: Given, ∫sinx-cosx2dx  We have to find the integral.

Q: T (b) fo 6 sin 20 cos² 20 ӨР

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Q: fip xp COS T 2. Oa) 2x sin(x) cos(2x) P-sin(2x) d- sin(x)+2x Osin(x) acer

A: y=cos (x2) We need to find dydx

Q: sin(2w)dw =

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Q: Sec (Cosx) dydx 1- Sin

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Q: Evaluate f æ° sin (ax²) dx оа. sin (az²) 2a2 z cos (az?) 2a +C b. sin (az?) 2a2 sin (az²) z cos…

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Q: Using appropriate substitution, sin³ (3x)cos*(3x)dx is equal to -cos"(3x) + cos"(3x) + c - cos (3x)…

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Q: -1 (3) cscx = sin X

A: We have to use proper substitutions and properties of analytic function.

Q: 3 .3 S sin 2xcos 2xdx

A: The objective is to solve the integration ∫sin32xcos32xdx Let, 2x=t⇒dx=12dt, then…

Q: 3. sin 3z cos 5z dr

A: Here we have to evaluate I=∫sin3xcos5xdx

Q: 25+16 x² (2, Sinx 3 + Cos? x xp 2

A: According to the fundamental theorem of calculus ∫f(x)dx=F(x), where dFdx=f(x). The definite…

Q: sin(7x 2) dx cos2 (7x 2)

A: Let u=cos(7x+2)differentiate both sides w.r.t. x.Use chain rule for cos(7x+2)From there we get du/-7…

Q: sec(2) tan(2) – 1 dz 3.

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Q: cos x sin x = csc 2x cos 3x sec 2x

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Q: b) S. cos x cos 7x dx

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Q: 1. (cos5 2x sin5 2x) dx 2. (tan5 4x tan² 2x sec2x)dx 3. (sin 5x cos 5x)dx

A: Step 1:1. I=∫(cos5(2x)sin5(2x))dxLet v=2x. Then dv=2dx, so 21​dv=2dx.Rewrite using u1 and…

Q: sin(3r) dr.

A: Given integral is,

Q: [17 sin³ x costx dx 5.

A: Given: I=∫17sin3xcos4x dx. To evaluate: Value of integral I.

Q: 22х+5 3. х2+20 dx

A: We have  (3) I=∫22x+5x2+20 dx We can write as I=22∫xx2+20+5∫ 1x2+20dxI=22I1+5I2

Q: 2) y = sin(3x²ex)

A: Find the derivative

Q: 2 sin x cos8x dx

A: Given- ∫0π2sin6xcos8xdx To Find- The value of the above integral. Identity Used- The value of the…

Q: 4. tan²B + 1 = sec² B

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Q: 4. sin 2x cos 2x dx

A: Here we integrate the given function.

Q: Find , if z= cos(3x² + 7y°) O 2x sin(3a? + 7y³) sin(3x² + 7y³) -9x cos(3x2 + 7y°) -6x sin(3x? + 7y°)

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Q: sin x dx + x cos² x 5.

A: Integral of a function is the anti derivative of the function, meaning area of the graph of the…

Q: a. y= 3(x³+4) b. y= cos-1(-3x)

A: we have to find dy/dx for given y

Q: 7. f sinx cos³ xdx

A: