Dr. J's Maths.com
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Trigonometric functions - Integration - basic.
Test Yourself 1.


 

Integrate the following indefinite integrals:

1. 2. 3.
4. 5. 6.
7. 8. 9. .
10. 11.  
  12.
13.
Hint.We cannot use the cos2 in the denominator.
So use the definition that one over cos2 is sec2.		 14.
Hint.Critically important strategy. We cannot do the integral directly. Use the trig identity
tan2x + 1 = sec2x.
The sec2 term then integrates directly to tan x.		 15. Find .
Hint.Critically important use of units. We cannot use calculus with degrees - ONLY with radians. Hence convert the x° to (xπ)/180. Then do the integration.

 

Evaluate the following definite integrals:
16.
Answer.3/8		 17.
Answer. 1/π.
 18.
Answer. 1.
19.
Answer. 1.
 20. Answer. 2.
 21.
Answer. 0.296.
22.
Answer. 2.
 23.
Answer.π/4 - 1		 24. Answer. 2/3 - π2/18.
25.
Answer.0		 26.
Answer.1 + 0.5 ln 2.		 27.
Answer.3(π/4 + 1)/2
28.
Answer. (3√2)/ 2.
 29.
(to 2 decimal places)
Answer.0.20		 30.
Answer.2√2(√2 - 1)

 

31. The gradient of the tangent function of a curve is given by
f '(x) = 3 sin 2x.

If the curve passes through (0, 0), find the equation of the curve.

 32. Use the trapezoidal Rule to evaluate

using 3 sub-intervals.

Answer.π2/4.