Dr. J's Maths.com
Where the techniques of Maths
are explained in simple terms.

Calculus - Integration - basic.
Test Yourself 1.

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The types of questions on this page which can be reached using the relevant hyperlinks are:

1. Finding primitives

2. Finding indefinite and definite integrals.

3. Finding the equations of curves.

4. Finding an approximate value.

NOTE: Answers to Q1-36 are in the solutions which cover all questions to 50 (see the end of this page for the hyperlink).

 

Find primitives of each of the following:

1. 6x - 2	2. 3x4 + 2x - 1	3. 2x-3 + 4x-2 +4x - 8x3
4.	5.	6. x-2(x-1 + 4 - 3x2)
7. (x - 1)(2x + 3)	8. (x + 2)(x2 - 3)	9. (x2 - 1)(x3 + 4)
10. (3x - 4)2	11. (15x - 42)20	12. (19 - 2x)3
13.	14.	15.

 

 

Integrate each of the following indefinite integrals:

16.	17.	18.
19.	20.	21.
22.	23.	24.
25.	26.	27.
28.	29.	30.
31.	32.	33.
34.	35.	36.

 

Evaluate each of the following definite integrals:

37. Answer.27.5.	38. Answer.-32/3.	39. Answer.0.
40. Answer.16/3.	41. If , find the value of a. Answer.a = 2.	42. Answer.1/8.
43. If , find the value of m. Answer.m = 16.	44. (leave your answer in exact form). Answer.I = 2√2 - 0.5.	45. Answer.I = 52/5.

 

Finding the equations of curves.

46.The gradient of a curve is 5 - 3x2. Determine the equation of the curve if it passes through the point (2, 3). Answer.f(x) = 5x - x3 + 1.	47. A curve y = f(x) has f "(x) = 18x + 10. Find f(x) if f(0) = 1 and f '(1) = 13. Answer.f(x) = 3x3 + 5x2 - 5x + 1.
48. The gradient function of a curve y = f(x) is given by . The curve passes through the point (1, 2). Find the equation of the curve. Answer.f(x) = 4x - 1/x - 1.	49.

Finding approximate values.

50. Given that , find an approximate value of π using four function values.