Trig - integ - Diff hence find TYS 1

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Trigonometric functions - Calculus - Differentiate ... hence find.
Test Yourself 1.

The questions on this page all require you:

1. to differentiate the first equation/expression; and

2. to use the results of that differentiation to determine the integral of another.

	1. (i) Differentiate x cosx. (ii) Hence evaluate . Answer.I = 1.	2. (i) Differentiate y = x² + 1. (ii) Hence find .
	3. (i) Differentiate sinx - x cos x. (ii) Hence find . Answer.I = 1.	4. By differentiating y = cos x, find .
	5.	6.
	7. Use the trigonometry identity to show that	8. (i) Differentiate y = x tan x. (ii) Hence find an expression for (also using the results of Q7).
	9. (i) Differentiate . (ii) Hence find . Answer.-3/4.	10. (i) Differentiate cos²(3x) with respect to x. (ii) Hence evaluate . Answer.(ii) Integral - 2.
	11.	12.
	13. (i) Show that tan³ x = tan x sec² x - tanx (ii) Hence find	14.
Applications	15. (i) Differentiate sin (x²). (ii) Use this result to find the exact area bounded by y = xcos (x²), the x axis and the lines x = 0 and x = 1.
	16. (i) By expressing cot x as prove that . (ii) Find the area of the region bounded by the curve y = cosec² x, the x axis and the lines π/6 and x = π/3.