3 (a) By method of substitution, evaluate the definite integral S =dx 2x² +1 (b) By method of substitution, evaluate the

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: 3 A By Method Of Substitution Evaluate The Definite Integral S Dx 2x 1 B By Method Of Substitution Evaluate The 1 (12.86 KiB) Viewed 34 times

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3 (a) By method of substitution, evaluate the definite integral S =dx 2x² +1 (b) By method of substitution, evaluate the definite integral -2 [x² str x² sin(x³)dx (4 marks) (4 marks)
4 Figure 4 shows a rectangle with perimeter 500 metres, i.e. 500 = 2x + 2y. X y Figure 4 (a) Prove that the area A of the rectangle is equal to following: A = 250x - x² (b) Using (a) or otherwise, find the value of x for making the maximum area. (4 marks) (6 marks)
(c) Check the result obtained in part (b) if it is a maximum length by using second derivative test. (d) Hence or otherwise, calculate the maximum area. (6 marks) (4 marks)