• tan°(x) Xp- cos“(x) 1 1 tan9

Q: Part A (i) Let f(x) = ln(3ª + 8"). Find f'(x). %3D (ii) Find 2" cos(r)` cos(2") d da

A: Derivative of function

Q: The function y sin a is also which of the following functions?

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Q: 7 cos?(x) sin(2x) dx

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Q: dr/dθ= cos (-5πθ), r(0)=9

A: Given,

Q: • 7/40 8000 sin (20x) Evaluate dx 7/60 1 – 2 cos (20x)

A: To evaluate: ∫π60π408000sin(20x)1-2cos(20x)dx...(1)

Q: Evaluate ㅠ * 0 sin (9x) sin(5x) dx.

A: To evaluate the following integral.∫0π sin9x sin5x dx

Q: 4x? )(i) Use the substitution x= tan e to show that sin? 20 dx. %3D (1+x*)' 4x2 (ii) Hence find in…

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Q: tan(0)=31/32

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Q: cos (E) U4+ tan(t)

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Q: 37/2 8 cos x dx T/2

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Q: S sin(bx) sec(bx) tan(bx) dx

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Q: 5cos³(x) sin(3–2x) answer in terms of sin and cos only ind the derivative of y = + tan²(3x² – 4x) –…

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Q: f(x) =-3 sin 3. Determine the amplitude, period and phase shift of the graph of f(x) for - 2r sxs…

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Q: Evaluate cos¹ (5x) sin(5x)dx + C

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Q: / [sec-(x) – csc²(x)]dr Evaluate: A e (x) - c«°(x) + C sec an(x) – cot(x) +C B esc (x) + sec³(x) + C…

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Q: 4 sin x dx (1 + cos x)²

A: Here we have to solve the given integration.

Q: Derive the formula tan¯¹(x) =_¹. dx 1+x²

A: Introduction: The derivative of a function is defined as the instantaneous rate of change of a…

Q: ∫sin5(6x)cos(6x)dx

A: ∫xn=xn+1n+1+C

Q: d(tan(x)) Using Euler’ formula, show that dx cos x 1.

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Q: π/4 IF ST/A tan (x) sec(x) dx = I, express the value of 。 π/4 tan (x) sec(x) dx in terms of I.

A: Given:- ∫0π4tan4xsecxdx=I

Q: T/4 35 (tan20tan + 1) sec20 d0 0

A: The integral is given by,

Q: •π/2 (cos x - sin x) dx

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Q: t/2 Find the value of sin(2x) sin(x) dx.

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Q: 2x sin-1(x²)dx =

A: This question is taken from the indefinite integral in which we have to choose the correct option…

Q: 7/2 SAT sin" x cos3 x dx

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Q: ㅠ (2 cos x - 2 sin x) dx

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Q: /2 97. 3 sin x cos x =dx VI + 3 sin²x

A: Integral problem

Q: 2 sin(2x) - 3 cos(x) dx

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Q: xdv S- le2cos(sin-w)

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Q: d -(cos(x² – 2x)) dx Evaluate

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Q: cos (1/x) dx ∞ o COS 21. 12

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