Hits: 83
Hits: 83 Question i. Show that . ii. Hence show that Solution i. We are given that; From this we can write; From this we can write; It can be formulated as; Hence; ii. We are required to show that; We have found in (i) that; Therefore; Rule for integration […]
Hits: 20 Question i. Show that . ii. Hence show that Solution i. We are given that; From this we can write; From this we can write; It can be formulated as; Hence; ii. We are required to show that; We have found in (i) that; Therefore; Rule for integration […]
Hits: 28 Question a. Find b. Show that Solution a. We are required to find; Rule for integration of , or ; b. We are required to show that; Rule for integration of is: This integral is valid only when . Division Rule; Power Rule; Please follow and like us: 0
Hits: 84 Question i. By differentiating , show that if θ then . ii. Hence show that Giving the values of a and b. iii. Find the exact value of Solution i. We are given that; We are required to show that; Since provided that ; Therefore; If […]
Hits: 39 Question i. Use the trapezium rule with 2 intervals to estimate the value of Giving your answer correct to 2 decimal places. ii. Find Solution i. We are required to apply Trapezium Rule to evaluate; The trapezium rule with intervals states that; We are given that there […]
Hits: 51 Question The diagram shows the curve , for . A rectangle OABC is drawn, where B is the point on the curve with x-coordinate , and A and C are on the axes, as shown. The shaded region R is bounded by the curve and by the lines x = and […]
Hits: 23 Question i. By differentiating , show that if θ then . ii. Hence show that Giving the values of a and b. iii. Find the exact value of Solution i. We are given that; We are required to show that; Since provided that ; Therefore; If […]
Hits: 27 Question i. Use the trapezium rule with 2 intervals to estimate the value of Giving your answer correct to 2 decimal places. ii. Find Solution i. We are required to apply Trapezium Rule to evaluate; The trapezium rule with intervals states that; We are given that there […]
Hits: 29 Question The diagram shows the curve , for . A rectangle OABC is drawn, where B is the point on the curve with x-coordinate , and A and C are on the axes, as shown. The shaded region R is bounded by the curve and by the lines x = and […]
Hits: 55 Question (i) Show that (2 sin x + cos x)2 can be written in the form (ii) Hence find the exact value of Solution i. We are given that; We have formula; Therefore; Therefore; Therefore; ii. We are required to find the exact value of; From (i) we […]
Hits: 39 Question The diagram shows the curve and its minimum point M. i. Show that the x-coordinate of M can be written in the form , where the value of a is to be stated. ii. Find the exact value of the area of the region enclosed by the curve […]
Hits: 35 Question (i) Show that and hence find the exact value of; (ii) The region enclosed by the curve y = tan x + cos x and the lines x = 0, and y = 0 is shown in the diagram. Find the exact volume of the solid produced when this region […]
Hits: 53 Question (i) Show that (2 sin x + cos x)2 can be written in the form (ii) Hence find the exact value of Solution i. We are given that; We have formula; Therefore; Therefore; Therefore; ii. We are required to find the exact value of; From […]
Hits: 43 Question The diagram shows the curve and its minimum point M. i. Show that the x-coordinate of M can be written in the form , where the value of a is to be stated. ii. Find the exact value of the area of the region enclosed by the curve […]
Hits: 24 Question i. Express in terms of . ii. Hence show that Solution i. We are given that; From this we can write; We have the trigonometric identity; From this we can write; Hence; ii. We are required to show that; We have found in (i) that; Therefore; […]
Hits: 45 Question Find the exact value of the positive constant k for which Solution We are given that; Rule for integration of , or ; Therefore; Let ; Therefore; Taking logarithm of both sides; Power Rule; Since ; Please follow and like us: 0
Hits: 26 Question i. By first expanding cos(2x + x), show that ii. Hence show that Solution i. We are given that and we are required to express as; Therefore; We have the trigonometric identity; From this we can write; Hence; ii. We are required to show that; […]
Hits: 29 Question The diagram shows the part of the curve for . Find the x-coordinates of the points on this part of the curve at which the gradient is 4. Solution We are required to find the x-coordinate of the points on the curve where gradient is 4. Therefore first we […]
Hits: 21 Question Show that Solution We are required to show that; Rule for integration of is: This integral is valid only when . Division Rule; Power Rule; Please follow and like us: 0
Hits: 19 Question a. Find the value of b. Find Solution a. We are required to find the value of; Rule for integration of is: b. We are required to find; Rule for integration of is: Rule for integration of , or ; Rule for integration of is: Please follow and […]
