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

Calculus - Integration - basic.
Test Yourself 2.

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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.

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

 

Find primitives/indefinite integrals of each of the following:

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

 

 

Integrate each of the following indefinite integrals:

16.	17.	18.
19.	20.	21.
22.	23.	24.
25.	26.	27.
28. (i) Prove that (ii) Hence or otherwise find	29.	30.
31.	32.	33. Use two different approaches to the following integration to show that:
34.	35.	36.

 

Evaluate each of the following definite integrals:

37. Answer.-4.5.	38. Answer.12	39. Answer.0.
40. Answer.23.47.	41. Answer.15/64.	42. If find the value of m. Answer.1/8.
43. If , find the value of m. Answer.m = 4.	44. If find the value of k. Answer.k = 0.8.	45. If find the value of h. Answer.h = ± √3.

 

Finding the equations of curves.

46. The graph of f(x) passes through the point (1, 3) and f '(x) = 3x2 - 2. Find f(x). Answer.f(x) = x3 - 2x + 4.	47. The graph of y = f(x) passes through the point (2, 12). The derivative function is f '(x) = 9x2 + 4. Find f(x). Answer.f(x) = 3x3 + 4x2 - 20.
48. The derivative of a function f(x) is f '(x) = 6x + 4. The line y = 10x - 5 is tangent to the graph of f(x). Find the function f(x). Answer.f(x) = 3x2 + 4x - 2.	49. If and when y =0, z = 1.5, find f(y).